Objection 1. It seems that children do not receive grace and virtues in Baptism. For grace and virtues are not possessed without faith and charity. But faith, as Augustine says (Ep. xcviii), "depends on the will of the believer": and in like manner charity depends on the will of the lover. Now children have not the use of the will, and consequently they have neither faith nor charity. Therefore children do not receive grace and virtues in Baptism.
Objection 2. Further, on John 14:12, "Greater than these shall he do," Augustine says that in order for the ungodly to be made righteous "Christ worketh in him, but not without him." But a child, through not having the use of free-will, does not co-operate with Christ unto its justification: indeed at times it does its best to resist. Therefore it is not justified by grace and virtues.
Objection 3. Further, it is written (Romans 4:5): "To him that worketh not, yet believing in Him that justifieth the ungodly, his faith is reputed to justice according to the purpose of the grace of God." But a child believeth not "in Him that justifieth the ungodly." Therefore a child receives neither sanctifying grace nor virtues.
Objection 4. Further, what is done with a carnal intention does not seem to have a spiritual effect. But sometimes children are taken to Baptism with a carnal intention, to wit, that their bodies may be healed. Therefore they do not receive the spiritual effect consisting in grace and virtue.
On the contrary, Augustine says (Enchiridion lii): "When little children are baptized, they die to that sin which they contracted in birth: so that to them also may be applied the words: 'We are buried together with Him by Baptism unto death'": (and he continues thus) "'that as Christ is risen from the dead by the glory of the Father, so we also may walk in newness of life.'" Now newness of life is through grace and virtues. Therefore children receive grace and virtues in Baptism.
I answer that, Some of the early writers held that children do not receive grace and virtues in Baptism, but that they receive the imprint of the character of Christ, by the power of which they receive grace and virtue when they arrive at the perfect age. But this is evidently false, for two reasons. First, because children, like adults, are made members of Christ in Baptism; hence they must, of necessity, receive an influx of grace and virtues from the Head. Secondly, because, if this were true, children that die after Baptism, would not come to eternal life; since according to Romans 6:23, "the grace of God is life everlasting." And consequently Baptism would not have profited them unto salvation.
Now the source of their error was that they did not recognize the distinction between habit and act. And so, seeing children to be incapable of acts of virtue, they thought that they had no virtues at all after Baptism. But this inability of children to act is not due to the absence of habits, but to an impediment on the part of the body: thus also when a man is asleep, though he may have the habits of virtue, yet is he hindered from virtuous acts through being asleep.
Reply to Objection 1. Faith and charity depend on man's will, yet so that the habits of these and other virtues require the power of the will which is in children; whereas acts of virtue require an act of the will, which is not in children. In this sense Augustine says in the book on Infant Baptism (Ep. xcviii): "The little child is made a believer, not as yet by that faith which depends on the will of the believer, but by the sacrament of faith itself," which causes the habit of faith.
Reply to Objection 2. As Augustine says in his book on Charity (Ep. Joan. ad Parth. iii), "no man is born of water and the Holy Ghost unwillingly which is to be understood not of little children but of adults." In like manner we are to understand as applying to adults, that man "without himself is not justified by Christ." Moreover, if little children who are about to be baptized resist as much as they can, "this is not imputed to them, since so little do they know what they do, that they seem not to do it at all": as Augustine says in a book on the Presence of God, addressed to Dardanus (Ep. clxxxvii).
Reply to Objection 3. As Augustine says (Serm. clxxvi): "Mother Church lends other feet to the little children that they may come; another heart that they may believe; another tongue that they may confess." So that children believe, not by their own act, but by the faith of the Church, which is applied to them: by the power of which faith, grace and virtues are bestowed on them.
Reply to Objection 4. The carnal intention of those who take children to be baptized does not hurt the latter, as neither does one's sin hurt another, unless he consent. Hence Augustine says in his letter to Boniface (Ep. xcviii): "Be not disturbed because some bring children to be baptized, not in the hope that they may be born again to eternal life by the spiritual grace, but because they think it to be a remedy whereby they may preserve or recover health. For they are not deprived of regeneration, through not being brought for this intention."
Source: Summa Theologica (New Advent)