ST. AMBROSE
“I hear you express grief because he [Valentinian] did not receive the Sacrament of Baptism. Tell me, what else is there in us except the will and petition? But he had long desired to be initiated... and expressed his intention to be baptized... Surely, he received [it] because he asked [for it].”

POPE INNOCENT III
Apostolicam:
 To your inquiry we respond thus: We assert without hesitation (on the authority of the holy Fathers Augustine and Ambrose) that the priest whom you indicated (in your letter) had died without the water of baptism, because he persevered in the faith of Holy Mother the Church and in the confession of the name of Christ, was freed from original sin and attained the joy of the heavenly fatherland. Read (brother) in the eighth book of Augustine’s City of God where among other things it is written, “Baptism is ministered invisibly to one whom not contempt of religion but death excludes.” Read again the book also of the blessed Ambrose concerning the death of Valentinian where he says the same thing. Therefore, to questions concerning the dead, you should hold the opinions of the learned Fathers, and in your church you should join in prayers and you should have sacrifices offered to God for the priest mentioned (Denzinger 388).
Debitum pastoralis officii, August 28, 1206:
 You have, to be sure, intimated that a certain Jєω, when at the point of death, since he lived only among Jєωs, immersed himself in water while saying: “I baptize myself in the name of the Father, and of the Son, and of the Holy Spirit. Amen.”
We respond that, since there should be a distinction between the one baptizing and the one baptized, as is clearly gathered from the words of the Lord, when He says to the Apostles: “Go baptize all nations in the name etc.” (cf. Matt. 28:19), the Jєω mentioned must be baptized again by another, that it may be shown that he who is baptized is one person, and he who baptizes another... If, however, such a one had died immediately, he would have rushed off to his heavenly home without delay because of the faith of the sacrament, although not because of the sacrament of faith (Denzinger 413).

ST. ALPHONSUS LIGUORI (1691-1787)
Moral Theology (Bk. 6):
“But baptism of desire is perfect conversion to God by contrition or love of God above all things accompanied by an explicit or implicit desire for true Baptism of water, the place of which it takes as to the remission of guilt, but not as to the impression of the [baptismal] character or as to the removal of all debt of punishment. It is called “of wind␅ [flaminis] because it takes place by the impulse of the Holy Ghost Who is called a wind [flamen]. Now it is de fide that men are also saved by Baptism of desire, by virtue of the Canon Apostolicam De Presbytero Non Baptizato and the Council of Trent, Session 6, Chapter 4, where it is said that no one can be saved “without the laver of regeneration or the desire for it.”