Objection 1. It would seem that Christ's Ascension into heaven belonged to Him according to His Divine Nature. For, it is written (Psalm 46:6): "God is ascended with jubilee": and (Deuteronomy 33:26): "He that is mounted upon the heaven is thy helper." But these words were spoken of God even before Christ's Incarnation. Therefore it belongs to Christ to ascend into heaven as God.
Objection 2. Further, it belongs to the same person to ascend into heaven as to descend from heaven, according to John 3:13: "No man hath ascended into heaven, but He that descended from heaven": and Ephesians 4:10: "He that descended is the same also that ascended." But Christ came down from heaven not as man, but as God: because previously His Nature in heaven was not human, but Divine. Therefore it seems that Christ ascended into heaven as God.
Objection 3. Further, by His Ascension Christ ascended to the Father. But it was not as man that He rose to equality with the Father; for in this respect He says: "He is greater than I," as is said in John 14:28. Therefore it seems that Christ ascended as God.
On the contrary, on Ephesians 4:10: "That He ascended, what is it, but because He also descended," a gloss says: "It is clear that He descended and ascended according to His humanity."
I answer that, The expression "according to" can denote two things; the condition of the one who ascends, and the cause of his ascension. When taken to express the condition of the one ascending, the Ascension in no wise belongs to Christ according to the condition of His Divine Nature; both because there is nothing higher than the Divine Nature to which He can ascend; and because ascension is local motion, a thing not in keeping with the Divine Nature, which is immovable and outside all place. Yet the Ascension is in keeping with Christ according to His human nature, which is limited by place, and can be the subject of motion. In this sense, then, we can say that Christ ascended into heaven as man, but not as God.
But if the phrase "according to" denote the cause of the Ascension, since Christ ascended into heaven in virtue of His Godhead, and not in virtue of His human nature, then it must be said that Christ ascended into heaven not as man, but as God. Hence Augustine says in a sermon on the Ascension: "It was our doing that the Son of man hung upon the cross; but it was His own doing that He ascended."
Reply to Objection 1. These utterances were spoken prophetically of God who was one day to become incarnate. Still it can be said that although to ascend does not belong to the Divine Nature properly, yet it can metaphorically; as, for instance, it is said "to ascend in the heart of man" (cf. Psalm 83:6), when his heart submits and humbles itself before God: and in the same way God is said to ascend metaphorically with regard to every creature, since He subjects it to Himself.
Reply to Objection 2. He who ascended is the same as He who descended. For Augustine says (De Symb. iv): "Who is it that descends? The God-Man. Who is it that ascends? The self-same God-Man." Nevertheless a twofold descent is attributed to Christ; one, whereby He is said to have descended from heaven, which is attributed to the God-Man according as He is God: for He is not to be understood as having descended by any local movement, but as having "emptied Himself," since "when He was in the form of God He took the form of a servant." For just as He is said to be emptied, not by losing His fulness, but because He took our littleness upon Himself, so likewise He is said to have descended from heaven, not that He deserted heaven, but because He assumed human nature in unity of person.
And there is another descent whereby He descended "into the lower regions of the earth," as is written Ephesians 4:9; and this is local descent: hence this belongs to Christ according to the condition of human nature.
Reply to Objection 3. Christ is said to ascend to the Father, inasmuch as He ascends to sit on the right hand of the Father; and this is befitting Christ in a measure according to His Divine Nature, and in a measure according to His human nature, as will be said later (58, 3)
Source: Summa Theologica (New Advent)