Part 7 - Crucifixion and Priapus.
Part 6 - From Wax Image to Exposed Body.
Part 5 - The First Crucifix.
Part 4 - The Tropaeum and the Furca.
Part 3 - Crux - Modern English Use and Ancient Quotidian Meanings.
Part 2 - Crux.
Well here is where the tradition of Jesus' Crown of Thorns comes from:
In Christianity, the Crown of Thorns, one of the instruments of the Passion, was woven of thorn branches and placed on Jesus Christ before his crucifixion. It is mentioned in the Canonical gospels of Matthew (27:29), Mark (15:17), and John (19:2, 5) and is often alluded to by the early Church Fathers, such as Clement of Alexandria, Origen, and others.John the Evangelist describes it thus (KJV, ch. 19):
"Then Pilate therefore took Jesus, and scourged him. And the soldiers plaited a crown of thorns, and put it on his head, and they put on him a purple robe, And said,"Hail, King of the Jews!" and they smote him with their hands. Pilate therefore went forth again, and saith unto them, Behold, I bring him forth to you, that ye may know that I find no fault in him. Then came Jesus forth, wearing the crown of thorns, and the purple robe. And Pilate saith unto them, Behold the man!"Wikipedia, Crown of Thorns.
A few writers of the first six centuries A.D. speak of a relic known to be still in existence and venerated by the faithful. St. Paulinus of Nola, writing after 409, refers to "the thorns with which Our Saviour was crowned" as relics held in honour along with the Cross to which he was nailed and the pillar at which he was scourged (Epistle Macarius in Migne, Patrologia Latina, LXI, 407). Cassiodorus (c. 570), when commenting on Psalm lxxxvi, speaks of the Crown of Thorns among the other relics which are the glory of the earthly Jerusalem. "There", he says, "we may behold the thorny crown, which was only set upon the head of Our Redeemer in order that all the thorns of the world might be gathered together and broken" (Migne, LXX, 621). When Gregory of Tours in De gloria martyri avers that the thorns in the Crown still looked green, a freshness which was miraculously renewed each day, he does not much strengthen the historical authenticity of a relic he had not seen, but the Breviarius, and the itinerary of Antoninus of Piacenza (6th century) clearly state that the Crown of Thorns was currently shown in the church on Mount Zion. From these fragments of evidence and others of later date (the "Pilgrimage" of the monk Bernard shows that the relic was still at Mount Sion in 870), it is likely that a purported Crown of Thorns was venerated at Jerusalem from the fifth century for several hundred years.
Wikipedia, Crown of Thorns - Jerusalem
The best way to figure that out is to go by the ancient writings and epigraphy to see whether to determine whether Romans bothered to place crowns of thorns on crucified convicts' heads, and whether early Christians believed Jesus wore his Crown of Thorns whilst hanging on his Cross.
B. Non-Christian Sources.
The first known epigraph, dated to the 1st C. CE, showing someone on a cross is the Pozzuoli Graffito. Note there is no crown of thorns on the person's head.
Next is the Alexamenos Graffito. late 2nd, early 3rd C. CE. It is commonly believed to represent the mockery of a certain Christian by the name of Alexamenos.  Note, too, there is no crown of thorns depicted here.
The above is an ancient magical amulet from Gaza, Syria-Palestina in the late 100s or early 200s CE. This is probably the oldest picture of Jesus on the cross. It is also non-Christian! At least how we moderns define "Christian," for in addition to:
ΥIE – - – ΠAT – - – HPIH – - – COΥX – - – PICTE
Orpheos Bakkikos amulet. Although scholarly consensus since Joh. Reil, Rob. Zahn and Otto Kern have considered it a forgery, a minority hold that is a genuine artifact from as early as the 2nd C. CE.  In favor of a possible authenticity, is an apparent horizontal element at crotch height that mimics the projection of a sedile behind the cross or tropaeum, and the fact that the stakes meant to secure the cross in the ground and upright look suspiciously phallic, judging by their top ends. Nota bene again, no crown of thorns.
The ancient non-Christian writers left behind literary evidence whether they applied a scarecrow wreath on crucified criminals' heads or not. Here's what I could find:
Catullus (84-54 BCE) has this to say:
Si, Comini, populi arbitrio tua cana senectusspurcata impurus moribus intereat,Non equidem dubito quin primum inimica bonorumlingua exsecta audio sit data vulturio,Effosos oculos uoret atro gutture cornuus,intestina canes, cetera membra lupi.If, by the will of the people, your old age Cominius,fouled by indecent behavior, came to be ended,I no doubt that your tongue -- such a good friend of evil!would be uprooted and fed to the greedy vulture,Nor that your gouged-out eyes glide down the raven's black gulletwhilst dogs took your bowels and wolves had the rest of you.Catullus, Carmina 108
'nec furtum feci nec fugi' si mihi dicitservus, 'habes pretium, loris non ureris,' aio.'non hominem occidi.' 'non pasces in crucem corvos'.If a slave were to say to me, "I never stole or ran away,"my reply would be, "You have your reward, you are not flogged.""I never killed anyone." "You will not feed crows on the cross."Q. Horatius Flaccus, Epistles, 1.16.46-48
vic turba vicatim hinc et hinc saxis petenscontundet obscaenos anus,post insepulta membra different lupiet Esquiline alitesneque hoc parentes, heu mihi superstites,effugerit spectaculum.The rabble, pelying you with stones on every side along every street, shall crush you, filthy hags. Then by then the wolves and the birds that haunt the esquiline shall scatter far and wide your unburied limbs, nor shall this sight escape my parents --- surviving me, alas!Q Horatius Flaccus Epode 5.101-106
Et quodcumque iacet nuda tellure cadaver,Ante feras volucresque sedet: nec carpere membraVult ferro manibusque suis, mosusque luporumExspectat, siccis raptura a faucibus artus.Where lay a corpse upon the naked earth,on ravening birds and beasts of prey the hag kept watch,not marred by knife or hand her spoil, till on his victim seized some hungry wolf,then dragged the morsel from his hungry fangs.Lucan, Pharsalia (Civil War) 6.550-553
vultur iumanto et canibus relictis
ad fetus properat partemque cadaveris adfert:
hic est ergo cibus magni quoque vulturis et se
pascentis, propria cum iam facit arbore nidos.
The vulture hurries from dead cattle and dogs and crosses
to bring some of the carrion of her offspring.
So this becomes the food of the vulture when he is full-grown
and feeds himself, making his nest in a tree of his own.
Juvenal, Satires 14.77-80
ut quidem uni suppliciter sepulturam precanti respondisse dicitur iam istum volucrum fore potestatem.For instance, to one man who begged humbly for burial, he is said to have replied, "The birds will soon settle that question."Suetonius, Lives of the Twelve Caesars, Augustus 13.2
ό Κρόνος ύπαγείω 'Αρης μεσουρανων νυκτός ποιουσιν εσταυρωμένους καί υπό όρνεων βεβρωμένους
Kronos at his nadir and Aries in mid heaven by night indicate those who are crucified and eaten by birds
Catalogus Codicum Graecorum VIII.4.p. 201, 22f 
γυμνοί γάρ σταυροϋνται καί τάς σάρκας άπολύουσιν οί σταυρωθένταςFor those crucified are crucified naked and lose their flesh to flesh-eating birds.Artemidorus, Oneirocriticon 2.53.7
...et patibuli cruciatum, cum canes et vultures protrahent viscera....and the torture of the patibulum, where dogs and vultures draw out her inmost parts.Lucius Apuleius, Metamorphoses, or, The Golden Asse. 6:32 fin.
άλλά πολϊται έμοί τόν έμέ ρεξαντα τοι αυτα θηρσί καί οίωνοϊς ζωόν άνεκρέμασαν.But for me the citizenry hanged up that one alive for the wild beasts and birds of prey because of what was done to me.'Collection of Ancient Greek Inscriptions in the British Museum IV, 2, no. 1036
B.3. Conclusions.στρεβλά κολαζόμενοι σκολοπηίδα μοίραν όρωσιν,πικροτάτοις κέντροισι προσαρτηθέντες εν ήλοις,οίωνων κακά δειπνα, κυνων δ' ελκύσματα δεινάPunished with limbs outstretched, they see the thorned stake as their lot,To the sharpest 'pegs' they are attached, with nails.Evil meals for birds, grim pickings for dogs.Pseudo Mantheo, Apotelesmatica 4.198
C. Christian Sources.
The above-cited Wikipedia article notes that some archaeologists have claimed to have seen a figure of the Crown of Thorns in the circle that surrounds the chresimon (chi-rho emblem) on early Christian sarcophagi, but the compliers considered that it was just as likely to have been a laurel wreath, as in the Sarcophagus Domatilla.
Ivory Sarcaphagus, British Museum, ca. 450 CE. No crown of thorns here, either.
Reliquarium, Lateran Crucifixion, ca. 600 CE. Note the short hair, full-length colobium, and no crown of thorns.
Santa Maria, Antiqua Roma, Crocifissione Fresco, ca. 741-52 CE. Again, a full-length colobium and no crown of thorns, maybe a single strand of thorns instead (see detail immediately above).
He who was Himself the Judge was judged by the Jews, falsely so called, and by Pilate the governor; was scourged, was smitten on the cheek, was spit upon; He wore a crown of thorns and a purple robe; He was condemned; He was crucified in reality, and not in appearance, not in imagination, not in deceit. He really died, and was buried, and rose from the dead, …”Ignatius of Antioch, Epistle to the Trallians 10
"For my death, which they think happened, (happened) to them in their error and blindness, since they nailed their man unto their death...It was another, their father, who drank the gall and the vinegar; it was not I. They struck me with the reed; it was another, Simon, who bore the cross on his shoulder. [I]t was another upon [w]hom they placed the crown of thorns... And I was laughing at their ignorance."
6. But having taken the Lord, running, they were pushing him and saying, 'Let us drag along the Son of God now that we have power over him.' 7. And they clothed him with purple and sat him on a chair of judgment, saying: 'Judge justly, King of Israel.' 8. And a certain one of them, having brought a thorny crown (στεφανον ακανθινον), put it on the head of the Lord. 9. And others who were standing there were spitting in his face, and others slapped his cheeks. Others were jabbing him with a reed; and some scourged him, saying, 'With such honor let us honor the Son of God.'Gospel of Peter 3:6-9
On perfumes and garlands.
Further, it were irrational in us, who have heard that the Lord was crowned with thorns, (Matthew 27:29) to crown ourselves with flowers, insulting thus the sacred passion of the Lord. For the Lord's crown prophetically pointed to us, who once were barren, but are placed around Him through the Church of which He is the Head. But it is also a type of faith, of life in respect of the substance of the wood, of joy in respect of the appellation of crown, of danger in respect of the thorn, for there is no approaching to the Word without blood....And they crowned Jesus raised aloft, testifying to their own ignorance. For being hard of heart, they understood not that this very thing, which they called the disgrace of the Lord, was a prophecy wisely uttered: “The Lord was not known by the people” (Isaiah 1:3) which erred, which was not circumcised in understanding, whose darkness was not enlightened, which knew not God, denied the Lord, forfeited the place of the true Israel, persecuted God, hoped to reduce the Word to disgrace; and Him whom they crucified as a malefactor they crowned as a king. Wherefore the Man on whom they believed not, they shall know to be the loving God the Lord, the Just. Whom they provoked to show Himself to be the Lord, to Him when lifted up they bore witness, by encircling Him, who is exalted above every name, with the diadem of righteousness by the ever-blooming thorn. This diadem, being hostile to those who plot against Him, coerces them; and friendly to those who form the Church, defends them. This crown is the flower of those who have believed on the glorified One, but covers with blood and chastises those who have not believed. It is a symbol, too, of the Lord's successful work, He having borne on His head, the princely part of His body, all our iniquities by which we were pierced.For He by His own passion rescued us from offenses, and sins, and such like thorns; and having destroyed the devil, deservedly said in triumph, “O Death, where is your sting?” (1 Corinthians 15:55) And we eat grapes from thorns, and figs from thistles; while those to whom He stretched forth His hands— the disobedient and unfruitful people— He lacerates into wounds. I can also show you another mystic meaning in it. For when the Almighty Lord of the universe began to legislate by the Word, and wished His power to be manifested to Moses, a godlike vision of light that had assumed a shape was shown him in the burning bush (the bush is a thorny plant); but when the Word ended the giving of the law and His stay with men, the Lord was again mystically crowned with thorn. On His departure from this world to the place whence He came, He repeated the beginning of His old descent, in order that the Word beheld at first in the bush, and afterwards taken up crowned by the thorn, might show the whole to be the work of one power, He Himself being one, the Son of the Father, who is truly one, the beginning and the end of time.Clement of Alexandria, The Instructor II.8 
...So with garlands; they are associated with revelling and drunkenness. Crowns of flowers strip the countryside and are bad for the head. Clement gives us a bit of ancient physiology about the coldness of the head. Flowers are lovely and in enjoying them we honor the Creator. ...To use flowers for garlands is to exploit them.; the flower and its beauty wither. ...The earliest Greeks, says Clement following Erasthenes, didn't use garlands; it was a degenerate practice which came in after the wars with Persia. The wreath sybolized freedom from care; hence its use for the dead. Further, to make wreaths of flowers for our living is to mock the Saviour's crown of thorns. The first revelation of God to Moses was in a burning thorn-bush. The revelation in Jesus is through a crown of thorns. The power is the one and the same. 
This “wood,” again, Isaac the son of Abraham personally carried for his own sacrifice, when God had enjoined that he should be made a victim to Himself. But, because these had been mysteries which were being kept for perfect fulfilment in the times of Christ, Isaac, on the one hand, with his “wood,” was reserved, the ram being offered which was caught by the horns in the bramble; Christ, on the other hand, in His times, carried His “wood” on His own shoulders, adhering to the horns of the cross, with a thorny crown encircling His head.Tertullian, Adversus Iudaeorum 13.21
And “the clouds were commanded not to rain a shower upon the vineyard of Sorek,” — the clouds being celestial benefits, which were commanded not to be forthcoming to the house of Israel; for it “had borne thorns”— whereof that house of Israel had wrought a crown for Christ— and not “ righteousness, but a clamour,”— the clamour whereby it had extorted His surrender to the cross.Tertullian, Adversus Iudaeorum 13.26
In short, what patriarch, what prophet, what Levite, or priest, or ruler, or at a later period what apostle, or preacher of the gospel, or bishop, do you ever find the wearer of a crown? I think not even the temple of God itself was crowned; as neither was the ark of the testament, nor the tabernacle of witness, nor the altar, nor the candlestick crowned though certainly, both on that first solemnity of the dedication, and in that second rejoicing for the restoration, crowning would have been most suitable if it were worthy of God. But if these things were figures of us (for we are temples of God, and altars, and lights, and sacred vessels), this too they in figure set forth, that the people of God ought not to be crowned. The reality must always correspond with the image. If, perhaps, you object that Christ Himself was crowned, to that you will get the brief reply: Be you too crowned, as He was; you have full permission. Yet even that crown of insolent ungodliness was not of any decree of the Jewish people. It was a device of the Roman soldiers, taken from the practice of the world—a practice which the people of God never allowed either on the occasion of public rejoicing or to gratify innate luxury: so they returned from the Babylonish captivity with timbrels, and flutes, and psalteries, more suitably than with crowns; and after eating and drinking, uncrowned, they rose up to play. Neither would the account of the rejoicing nor the exposure of the luxury have been silent touching the honour or dishonour of the crown. Thus too Isaiah, as he says, “With timbrels, and psalteries, and flutes they drink wine,” (Isaiah 5:12) would have added “with crowns,” if this practice had ever had place in the things of God.Tertullian, De corona (The Chaplet) 9: 80b-84a
But He that is both the Head of the man, and the Beauty of the woman, the Husband of the Church, Christ Jesus, what sort of crown, I pray thee, did He put on for both man and woman? 'Twas one, methinks, of thorns and briers, as a figure of those sins, which the earth of our flesh hath brought forth unto us, but the power of the Cross hath taken away, overcoming the sharpness of every sting of death, in the sufferings of the head of the Lord. Surely, setting aside the figure, there is on the face of it mockery, and debasement, and dishonour, and mixed with these cruelty, which then defiled and tore the brow of the Lord, that thou mayest now be crowned with thy laurel, and thy myrtle, and thy olive, and every famous branch, and what is of more frequent use, with roses also of an hundred leaves culled from the garden of Midas, and lilies of either kind, and every sort of violets, even with jewels perchance and gold, that thou mayest rival also that crown of Christ, which came unto Him afterwards, because it was after the gall that He tasted the honey also, nor was He saluted as the King of Glory by the hosts of Heaven, before He had been proscribed upon the cross as the King of the Jews. Being first made by the Father a little lower than the angels, and so crowned with glory and worship. If for these things thou owest thy head to Him, pay Him if thou canst with such an head as His own was, when He offered it up for thine: or wear not a crown of flowers, if thou art not able to wear one of thorns; for thou art able not to wear one of flowers.Tertullian, De corona (The Chaplet) 15: 149b-155a
306. The Lord, in putting on the "scarlet robe," took the blood of the world on himself; and in that "crown of thorns" he received the thorns of our sins woven into his head (cf. Mt 27:28-29). Of the scarlet robe, it is written that "they stripped him of the robe" (Mt 27:31), but of the crown of thorns, the evangelists wrote no such thing because they wanted us to ask what happened with the crown of thorns which was placed on him at one point and never removed. It is my opinion that the crown of thorns was consumed by the head of Jesus so that they are now no longer our old thorns, once Jesus has taken them from us and put them on his sacred head. 
The Crowning with Thorns:Origen writes that this crown of thorns was not taken from the head of the Lord until he had expired upon the cross. (Corona spinea, semel imposita, et nunquam detracta)