It's clear Aquinas had way, way, way too much time on his hands...
Objection 1:
It seems that no man can be saved without Baptism. For our Lord said (Jn. 3:5): "Unless a man be born again of water and the Holy Ghost, he cannot enter the kingdom of God." But those alone are saved who enter God's kingdom. Therefore none can be saved without Baptism, by which a man is born again of water and the Holy Ghost.
Aquinas starts out wrong here with baptism...We are not born again of water and the Spirit...We are already born of water, now we need to be born of the Spirit...
Objection 2:
Further, in the book De Eccl. Dogm. xli, it is written: "We believe that no catechumen, though he die in his good works, will have eternal life, except he suffer martyrdom, which contains all the sacramental virtue of Baptism." But if it were possible for anyone to be saved without Baptism, this would be the case specially with catechumens who are credited with good works, for they seem to have the "faith that worketh by charity" (Gal. 5:6). Therefore it seems that none can be saved without Baptism.
Here, Aquinas claims that if you are not baptized physically, you can still go to heaven if you were killed for your Christianity, as long as you did good works...
Kind of impossible to square that with scripture...
Objection 3:
Further, as stated above (A[1]; Q[65], A[4]), the sacrament of Baptism is necessary for salvation. Now that is necessary "without which something cannot be" (Metaph. v). Therefore it seems that none can obtain salvation without Baptism.
On the contrary, Augustine says (Super Levit. lxxxiv) that "some have received the invisible sanctification without visible sacraments, and to their profit; but though it is possible to have the visible sanctification, consisting in a visible sacrament, without the invisible sanctification, it will be to no profit." Since, therefore, the sacrament of Baptism pertains to the visible sanctification, it seems that a man can obtain salvation without the sacrament of Baptism, by means of the invisible sanctification.
Augustine is on the right track but he eventually jumps the track...
I answer that, The sacrament or Baptism may be wanting to someone in two ways. First, both in reality and in desire; as is the case with those who neither are baptized, nor wished to be baptized: which clearly indicates contempt of the sacrament, in regard to those who have the use of the free-will. Consequently those to whom Baptism is wanting thus, cannot obtain salvation: since neither sacramentally nor mentally are they incorporated in Christ, through Whom alone can salvation be obtained.
Aquinas is right on the edge, but he never gets it...
Secondly, the sacrament of Baptism may be wanting to anyone in reality but not in desire: for instance, when a man wishes to be baptized, but by some ill-chance he is forestalled by death before receiving Baptism. And such a man can obtain salvation without being actually baptized, on account of his desire for Baptism, which desire is the outcome of "faith that worketh by charity," whereby God, Whose power is not tied to visible sacraments, sanctifies man inwardly. Hence Ambrose says of Valentinian, who died while yet a catechumen: "I lost him whom I was to regenerate: but he did not lose the grace he prayed for."
It's the blind leading the blind, one after another like dominos
Reply to Objection 1: As it is written (1 Kings 16:7), "man seeth those things that appear, but the Lord beholdeth the heart." Now a man who desires to be "born again of water and the Holy Ghost" by Baptism, is regenerated in heart though not in body. thus the Apostle says (Rom. 2:29) that "the circumcision is that of the heart, in the spirit, not in the letter; whose praise is not of men but of God."
Aquinas has got it here but he don't know what he's got...
Reply to Objection 2: No man obtains eternal life unless he be free from all guilt and debt of punishment. Now this plenary absolution is given when a man receives Baptism, or suffers martyrdom:
Aquinas blew it here...He's just as blind as a bat coming in backwards...
for which reason is it stated that martyrdom "contains all the sacramental virtue of Baptism," i.e. as to the full deliverance from guilt and punishment. Suppose, therefore, a catechumen to have the desire for Baptism (else he could not be said to die in his good works, which cannot be without "faith that worketh by charity"), such a one, were he to die, would not forthwith come to eternal life, but would suffer punishment for his past sins, "but he himself shall be saved, yet so as by fire" as is stated 1 Cor. 3:15.
And of course, Aquinas mis-quotes the verse to justify his theology...The fire didn't burn the Christian, it burned his bad works...
Reply to Objection 3: The sacrament of Baptism is said to be necessary for salvation in so far as man cannot be saved without, at least, Baptism of desire; "which, with God, counts for the deed" (Augustine, Enarr. in Ps. 57).
There it is in a nutshell...But it flew right past Aquinas...It was too high over his head to reach it...
The real Baptism of Desire in the scriptures results in a Spiritual Baptism...No water involved...Aquinas talks about it but he doesn't get it...
If one comes to Jesus and says, 'Lord, I'm coming to you the only way I know how, please take me, it's a done deal...That initiates the baptism of desire...No water...
Jesus performs an operation...A spiritual operation...A circumcision...A circumcision of the heart...
Your new man is killed, buried and resurrected...Your old man (your flesh) is still there...But it's not connected...
Here's Aquinas again:
a man who desires to be "born again of water and the Holy Ghost" by Baptism, is regenerated in heart though not in body. thus the Apostle says (Rom. 2:29) that "the circumcision is that of the heart, in the spirit, not in the letter; whose praise is not of men but of God."
Born again of water is not scriptural...Aquinas added that to make baptism mean water baptism...If he would have left out the water, Aquinas would have gotten the baptism of the Holy Ghost, but he missed it...
Reading him to find out how very wrong he is will obstruct a lot of understanding. Reading the questions just to find the answers is the wrong way to go about getting anything out of it.