Someone has recently told me that St. Thomas thought that the resurrected body that awaits those who are saved, like Jesus’ resurrected body, is not composed of the very same material as the mortal body. This person said that the resurrected body would be like the angels’ bodies and be mostly invisible and intangible, but can at times be made visible and tangible in some way. Such bodies are in some sense spiritual but can be given a physical aspect under certain conditions.
Saint Thomas Aquinas does not believe any of the things which you say were ascribed to “St. Thomas.” First, the resurrected body of both Christ and the Blessed are the very same material bodies they had before they died.
Christ’s body fell by death; namely, inasmuch as the soul which was its formal perfection was separated from it. Hence, in order for it to be a true resurrection, it was necessary for the same body of Christ to be once more united with the same soul. And since the truth of the body’s nature is from its form it follows that Christ’s body after His Resurrection was a true body, and of the same nature as it was before.Summa Theologiae III, 54, 1
But Christ’s body after the Resurrection was truly made up of elements, and had tangible qualities such as the nature of a human body requires, and therefore it could naturally be handled.Summa Theologiae III, 54, 2 ad 2
The resurrected body is not spiritual by being made out of, or turned into, a spiritual substance. It is spiritual by being completely subject to the spirit (soul) of its possessor.
But such is the disposition of a glorified body that it is spiritual, i.e. subject to the spirit, as the Apostle says (1 Cor. 15:44). Now in order for the body to be entirely subject to the spirit, it is necessary for the body’s every action to be subject to the will of the spirit. Again, that an object be seen is due to the action of the visible object upon the sight, as the Philosopher shows (De Anima ii). Consequently, whoever has a glorified body has it in his power to be seen when he so wishes, and not to be seen when he does not wish it.Summa Theologiae III, 54, 1 ad 2
For certain heretics, as Augustine relates (De Civ. Dei xiii, 22), ascribed to [glorified bodies] the subtlety whereby spiritual substances are said to be subtle: and they said that at the resurrection the body will be transformed into a spirit, and that for this reason the Apostle describes as being “spiritual” the bodies of those who rise again (1 Cor. 15:44). But this cannot be maintained. First, because a body cannot be changed into a spirit, since there is no community of matter between them. … Hence others say that the aforesaid completeness by reason of which human bodies are said to be subtle will result from the dominion of the glorified soul (which is the form of the body) over the body, by reason of which dominion the glorified body is said to be “spiritual,” as being wholly subject to the spirit.”Summa Theologiae Supplement, 83, 1
In response to the most outrageous claim, the Angelic Doctor (Aquinas) would never have thought that angels have bodies!! On the manner in which angels make use of material bodies, see the essay Angels.