There is not enough time in the day to refute the Dimondite errors doing the rounds on this thread. I really do not currently have the means, ability or inclination to refute this all over again, but this thread contains enough temerarious accusations against the Doctors of the Church and the Popes who specifically approved their teaching and made it their own to compel me to respond.
1. First, to the bizarre claim that the Magisterium has never taught that Baptism of Desire supplies the remission of sins but not necessarily the remission of the entire debt of punishment, the other letter (Dz. 388), possibly penned according to some scholars by the same Innocent III clearly teaches this, saying the soul invalidly baptized who was saved by Baptism of Desire is in purgatory, since it is for this reason alone, that prayers are necessary for him.
So what is Innocent III teaching in the letter cited on this thread? He is saying that, this soul will not fall into hell, but will "fly" to heaven. As for "without delay", there was an error that said no soul will enter heaven until the last judgment, but be in an eternal limbo-like state until then. Cardinals and others later than Innocent III fell into that error, and that is what Innocent III appears to be teaching against.
2. Second, it is also indicated in the passage in St. Ambrose. Throughout Christian history, for centuries everyone understood that Valentian was saved by obtaining justification through desire. Fr. Feeney was the first to speculate otherwise, claiming that Valentian had received actual Baptism. But this is disproved by the passage itself, which says that the mysteries were not solemnly celebrated (which in the case of someone actually baptized, they would be), and St. Ambrose prays for his soul at his funeral (which all understood one does not do, either for those actually baptized, or for martyrs), proving again he was in purgatory. Finally, St. Ambrose says "if martyrs are washed in their own blood, his piety and devotedness have washed him also".
3. Third, contrary to Feeneyite absurdities, the Roman Catechism and the Fathers of Trent follow St. Thomas in describing Baptism of Desire almost word for word. Exactly like him, they distinguish between adults and infants, giving the same illustrations and Scriptural examples. They say infants have no other means of salvation than actual Baptism, and so will be lost if they die, thus the danger of dying and going to hell is present. For adults, this same danger is not present, because adults can obtain grace and justice through their intention to receive baptism, combined with repentance for past sins, when it is impossible to be washed in the "salutary waters" of baptism without their own fault. This clearly teaches these persons will not be eternally lost, and thus pre-emptively condemns Feeneyism in all its forms.
4. To the ridiculous but anticipated objection that this is not infallible, it is answered that the Roman Catechism clearly shows us the mind of the Tridentine Fathers. If they taught us there that adult souls can be saved through the desire of baptism, that is obviously what they intended to define in Trent. If only solemn definitions will be admitted, there are two easy proofs of this doctrine from the same.
First, that voto never refers to a disposition in receiving the actual sacrament, voto always refers to the reception of the sacramental effect in desire. This proves that where Trent talks about the voto of Baptism, it is defining the Baptism of desire. In Trent itself, voto in reference to penance and the Eucharist refers to the perfect contrition and the spiritual communion, as even Feeneyites concede. I challenge anyone to prove that voto ever refers to a disposition anywhere. All your errors come from a lack of knowledge of St. Thomas, or in some cases even of Latin. Pope St. Pius X warns you that you cannot understand even the language in which the Church proposes Her dogmas if you are ignorant of St. Thomas. If you don't know in other words what voto means in St. Thomas, you won't know what it means in Trent.
5. Second, where Trent clearly defines dogmatically that the sacraments necessary for salvation are necessary in fact or in desire. It proscribes that "without them, or without the desire thereof, men obtain of God ... the grace of justification". Clearly proving, again evident in the Latin, that the grace of justification can be received in desire for two sacraments. Again Feeneyites admit this in the case of penance, but absurdly deny the plural proves that the grace of justification can be received through the desire of both sacraments necessary for salvation, namely in Trent baptism and penance.
Again, contrary to the errors above, the Roman Catechism specifically says elsewhere that in penance, we recover the grace of Baptism. Proving once more that the proper grace of Baptism is naught other than the grace of justification. It is a plainly condemned error, in the canons of Trent, that pretends that the grace of justification necessarily and intrinsically remits also the entire debt of punishment. Not even Feeneyites can contest this. After teaching this doctrine in the Roman Catechism, St. Pius V proscribed the errors of the heretic Michael Baius that the remission of sins can only be obtained in the laver of baptism, and that charity in catechumens cannot avail toward this end.
Post-Trent, over a dozen Popes have infallibly declared the doctrine taught in St. Alphonsus' Theologia Moralis to be safe and irreformable, reaffirming also this specific doctrine by their own authority. Pope St. Pius X for example teaches Baptism of Desire is an act of perfect love of God, or contrition, and everybody knows contrition, combined with the desire to do all that God wills - through the operation of the actual sacrament in desire - effects justification but not necessarily the remission of the entire debt of punishment. Hence, those saved by baptism of desire will as a rule go to purgatory.