Objection 1. It would seem that it was not fitting that Christ should be transfigured. For it is not fitting for a true body to be changed into various shapes [figuras, but only for an imaginary body. Now Christ's body was not imaginary, but real, as stated above (Question 5, Article 1). Therefore it seems that it should not have been transfigured.
Objection 2. Further, figure is in the fourth species of quality, whereas clarity is in the third, since it is a sensible quality. Therefore Christ's assuming clarity should not be called a transfiguration.
Objection 3. Further, a glorified body has four gifts, as we shall state farther on (XP, 82), viz. impassibility, agility, subtlety, and clarity. Therefore His transfiguration should not have consisted in an assumption of clarity rather than of the other gifts.
On the contrary, It is written (Matthew 17:2) that Jesus "was transfigured" in the presence of three of His disciples.
I answer that, Our Lord, after foretelling His Passion to His disciples, had exhorted them to follow the path of His sufferings (Matthew 16:21-24). Now in order that anyone go straight along a road, he must have some knowledge of the end: thus an archer will not shoot the arrow straight unless he first see the target. Hence Thomas said (John 14:5): "Lord, we know not whither Thou goest; and how can we know the way?" Above all is this necessary when hard and rough is the road, heavy the going, but delightful the end. Now by His Passion Christ achieved glory, not only of His soul, not only of His soul, which He had from the first moment of His conception, but also of His body; according to Luke (24:26): "Christ ought [Vulgate: 'ought not Christ'] to have suffered these things, and so to enter into His glory (?)." To which glory He brings those who follow the footsteps of His Passion, according to Acts 14:21: "Through many tribulations we must enter into the kingdom of God." Therefore it was fitting that He should show His disciples the glory of His clarity (which is to be transfigured), to which He will configure those who are His; according to Philippians 3:21: "(Who) will reform the body of our lowness configured [Douay: 'made like'] to the body of His glory." Hence Bede says on Mark 8:39: "By His loving foresight He allowed them to taste for a short time the contemplation of eternal joy, so that they might bear persecution bravely."
Reply to Objection 1. As Jerome says on Matthew 17:2: "Let no one suppose that Christ," through being said to be transfigured, "laid aside His natural shape and countenance, or substituted an imaginary or aerial body for His real body. The Evangelist describes the manner of His transfiguration when he says: 'His face did shine as the sun, and His garments became white as snow.' Brightness of face and whiteness of garments argue not a change of substance, but a putting on of glory."
Reply to Objection 2. Figure is seen in the outline of a body, for it is "that which is enclosed by one or more boundaries" [Euclid, bk i, def. xiv]. Therefore whatever has to do with the outline of a body seems to pertain to the figure. Now the clarity, just as the color, of a non-transparent body is seen on its surface, and consequently the assumption of clarity is called transfiguration.
Reply to Objection 3. Of those four gifts, clarity alone is a quality of the very person in himself; whereas the other three are not perceptible, save in some action or movement, or in some passion. Christ, then, did show in Himself certain indications of those three gifts--of agility, for instance, when He walked on the waves of the sea; of subtlety, when He came forth from the closed womb of the Virgin; of impassibility, when He escaped unhurt from the hands of the Jews who wished to hurl Him down or to stone Him. And yet He is not said, on account of this, to be transfigured, but only on account of clarity, which pertains to the aspect of His Person.
Source: Summa Theologica (New Advent)