What is the exact nature of Aquinas's private revelation of Jesus to him?

What is the exact nature of Aquinas's private revelation of Jesus to him?

It seems evident that this was a corporal vision and not a intellectual vision or imaginative vision. It certainly was not the Beatific Vision because St. Thomas had not yet died and entered the presence of God.

Seeing that the conversation was heard by another friar, it makes sense that it was a corporal vision.

Corporeal vision

Corporeal vision is a supernatural manifestation of an object to the eyes of the body. It may take place in two ways: either a figure really present strikes the retina and there determines the physical phenomenon of the vision, or an agent superior to man directly modifies the visual organ and produces in the composite a sensation equivalent to that which an external object would produce. According to the authorities the first is the usual manner; it corresponds to the invincible belief of the seer, e.g. Bernadette at Lourdes; it implies a minimum of miraculous intervention if the vision is prolonged or if it is common to several persons. But the presence of an external figure may be understood in two ways. Sometimes the very substance of the being or the person will be presented; sometimes it will be merely an appearance consisting in a certain arrangement of luminous rays. The first may be true of living persons and even, it would seem, of the now glorious bodies of Christ and the Blessed Virgin, which by the eminently probable supernatural phenomenon of multilocation may become present to men without leaving the abode of glory. The second is realized in the corporeal apparition of the unresurrected dead or of pure spirits.

St. Thomas Aquinas explains in his Summa Theologiae Question 174 on the The division of prophecy, the various types of visions are implied here.

Whether the degrees of prophecy can be distinguished according to the imaginary vision?

As stated above (II-II:173:2), the prophecy wherein, by the intelligible light, a supernatural truth is revealed through an imaginary vision, holds the mean between the prophecy wherein a supernatural truth is revealed without imaginary vision, and that wherein through the intelligible light and without an imaginary vision, man is directed to know or do things pertaining to human conduct. Now knowledge is more proper to prophecy than is action; wherefore the lowest degree of prophecy is when a man, by an inward instinct, is moved to perform some outward action. Thus it is related of Samson (Judges 15:14) that "the Spirit of the Lord came strongly upon him, and as the flax ['Lina.' St. Thomas apparently read 'ligna' ('wood')] is wont to be consumed at the approach of fire, so the bands with which he was bound were broken and loosed." The second degree of prophecy is when a man is enlightened by an inward light so as to know certain things, which, however, do not go beyond the bounds of natural knowledge: thus it is related of Solomon (1 Kings 4:32-33) that "he spoke . . . parables . . . and he treated about trees from the cedar that is in Libanus unto the hyssop that cometh out of the wall, and he discoursed of beasts and of fowls, and of creeping things and of fishes": and all of this came from divine inspiration, for it was stated previously (1 Kings 4:29): "God gave to Solomon wisdom and understanding exceeding much."

Nevertheless these two degrees are beneath prophecy properly so called, because they do not attain to supernatural truth. The prophecy wherein supernatural truth is manifested through imaginary vision is differentiated first according to the difference between dreams which occur during sleep, and vision which occurs while one is awake. The latter belongs to a higher degree of prophecy, since the prophetic light that draws the soul away to supernatural things while it is awake and occupied with sensible things would seem to be stronger than that which finds a man's soul asleep and withdrawn from objects of sense. Secondly the degrees of this prophecy are differentiated according to the expressiveness of the imaginary signs whereby the intelligible truth is conveyed. And since words are the most expressive signs of intelligible truth, it would seem to be a higher degree of prophecy when the prophet, whether awake or asleep, hears words expressive of an intelligible truth, than when he sees things significative of truth, for instance "the seven full ears of corn" signified "seven years of plenty" (Genesis 41:22-26). On such like signs prophecy would seem to be the more excellent, according as the signs are more expressive, for instance when Jeremias saw the burning of the city under the figure of a boiling cauldron (Jeremiah 1:13). Thirdly, it is evidently a still higher degree of prophecy when a prophet not only sees signs of words or deeds, but also, either awake or asleep, sees someone speaking or showing something to him, since this proves the prophet's mind to have approached nearer to the cause of the revelation. Fourthly, the height of a degree of prophecy may be measured according to the appearance of the person seen: for it is a higher degree of prophecy, if he who speaks or shows something to the waking or sleeping prophet be seen by him under the form of an angel, than if he be seen by him under the form of man: and higher still is it, if he be seen by the prophet whether asleep or awake, under the appearance of God, according to Isaiah 6:1, "I saw the Lord sitting."

But above all these degrees there is a third kind of prophecy, wherein an intelligible and supernatural truth is shown without any imaginary vision. However, this goes beyond the bounds of prophecy properly so called, as stated above (Article 2, Reply to Objection 3); and consequently the degrees of prophecy are properly distinguished according to imaginary vision.

St. Thomas obviously had a vision which is a ”supernatural perception of some object that is not visible naturally. A vision is a revelation only when the object seen also discloses some hidden truth or mystery.” In this sense Thomas Aquinas had a mystical experience.