Objection 1. It would seem that the souls in question suffer spiritual affliction on account of the state wherein they are, because as Chrysostom says (Hom. xxiii in Matth.), the punishment of God in that they will be deprived of seeing God will be more painful than their being burned in hell fire. Now these souls will be deprived of seeing God. Therefore they will suffer spiritual affliction thereby.
Objection 2. Further, one cannot, without suffering, lack what one wishes to have. But these souls would wish to have the divine vision, else their will would be actually perverse. Therefore since they are deprived of it, seemingly they also suffer.
Objection 3. Further, if it be said that they do not suffer, because they know that through no fault of theirs they are deprived thereof, on the contrary: Freedom from fault does not lessen but increases the pain of punishment: for a man does not grieve less for that he is disinherited or deprived of a limb through no fault of his. Therefore these souls likewise, albeit deprived of so great a good through no fault of theirs, suffer none the less.
Objection 4. Further, as baptized children are in relation to the merit of Christ, so are unbaptized children to the demerit of Adam. But baptized children receive the reward of eternal life by virtue of Christ's merit. Therefore the unbaptized suffer pain through being deprived of eternal life on account of Adam's demerit.
Objection 5. Further, separation from what we love cannot be without pain. But these children will have natural knowledge of God, and for that very reason will love Him naturally. Therefore since they are separated from Him for ever, seemingly they cannot undergo this separation without pain.
On the contrary, If unbaptized children have interior sorrow after death, they will grieve either for their sin or for their punishment. If for their sin, since they cannot be further cleansed from that sin, their sorrow will lead them to despair. Now sorrow of this kind in the damned is the worm of conscience. Therefore these children will have the worm of conscience, and consequently theirs would not be the mildest punishment, as Augustine says it is [See 1, "On the contrary"]. If, on the other hand, they grieve for their punishment, it follows, since their punishment is justly inflicted by God, that their will opposes itself to divine justice, and thus would be actually inordinate, which is not to be granted. Therefore they will feel no sorrow.
Further, right reason does not allow one to be disturbed on account of what one was unable to avoid; hence Seneca proves (Ep. lxxxv, and De ira ii, 6) that "a wise man is not disturbed." Now in these children there is right reason deflected by no actual sin. Therefore they will not be disturbed for that they undergo this punishment which they could nowise avoid.
I answer that, on this question there are three opinions. Some say that these children will suffer no pain, because their reason will be so much in the dark that they will not know that they lack what they have lost. It, however, seems improbable that the soul freed from its bodily burden should ignore things which, to say the least, reason is able to explore, and many more besides. Hence others say that they have perfect knowledge of things subject to natural reason, and know God, and that they are deprived of seeing Him, and that they feel some kind of sorrow on this account but that their sorrow will be mitigated, in so far as it was not by their will that they incurred the sin for which they are condemned. Yet this again would seem improbable, because this sorrow cannot be little for the loss of so great a good, especially without the hope of recovery: wherefore their punishment would not be the mildest. Moreover the very same reason that impugns their being punished with pain of sense, as afflicting them from without, argues against their feeling sorrow within, because the pain of punishment corresponds to the pleasure of sin; wherefore, since original sin is void of pleasure, its punishment is free of all pain. Consequently others say that they will know perfectly things subject to natural knowledge, and both the fact of their being deprived of eternal life and the reason for this privation, and that nevertheless this knowledge will not cause any sorrow in them. How this may be possible we must explore.
Accordingly, it must be observed that if one is guided by right reason one does not grieve through being deprived of what is beyond one's power to obtain, but only through lack of that which, in some way, one is capable of obtaining. Thus no wise man grieves for being unable to fly like a bird, or for that he is not a king or an emperor, since these things are not due to him; whereas he would grieve if he lacked that to which he had some kind of claim. I say, then, that every man who has the use of free-will is adapted to obtain eternal life, because he can prepare himself for grace whereby to merit eternal life [Cf. I-II, 109, 5 and 6]; so that if he fail in this, his grief will be very great, since he has lost what he was able to possess. But children were never adapted to possess eternal life, since neither was this due to them by virtue of their natural principles, for it surpasses the entire faculty of nature, nor could they perform acts of their own whereby to obtain so great a good. Hence they will nowise grieve for being deprived of the divine vision; nay, rather will they rejoice for that they will have a large share of God's goodness and their own natural perfections. Nor can it be said that they were adapted to obtain eternal life, not indeed by their own action, but by the actions of others around them, since they could be baptized by others, like other children of the same condition who have been baptized and obtained eternal life: for this is of superabundant grace that one should be rewarded without any act of one's own. Wherefore the lack of such a grace will not cause sorrow in children who die without Baptism, any more than the lack of many graces accorded to others of the same condition makes a wise man to grieve.
Reply to Objection 1. In those who, having the use of free-will, are damned for actual sin, there was aptitude to obtain eternal life, but not in children, as stated above. Consequently there is no parity between the two.
Reply to Objection 2. Although the will may be directed both to the possible and to the impossible as stated in Ethic. iii, 5, an ordinate and complete will is only of things which in some way are proportionate to our capability; and we grieve if we fail to obtain this will, but not if we fail in the will that is of impossibilities, and which should be called "velleity" [Cf. I-II, 13, 5, ad 1; III, 21, 4] rather than "will"; for one does not will such things absolutely, but one would if they were possible.
Reply to Objection 3. Everyone has a claim to his own inheritance or bodily members, wherefore it is not strange that he should grieve at their loss, whether this be through his own or another's fault: hence it is clear that the argument is not based on a true comparison.
Reply to Objection 4. The gift of Christ surpasses the sin of Adam, as stated in Romans 5:15, seqq.. Hence it does not follow that unbaptized children have as much of evil as the baptized have of good.
Reply to Objection 5. Although unbaptized children are separated from God as regards the union of glory, they are not utterly separated from Him: in fact they are united to Him by their share of natural goods, and so will also be able to rejoice in Him by their natural knowledge and love.
Source: Summa Theologica (New Advent)