But it is Schadenfreude, a mischievous delight in the misfortunes of others, which remains the worst trait in human nature. It is a feeling which is closely akin to cruelty, and differs from it, to say the truth, only as theory from practice. In general, it may be said that it takes the place which pity ought to take -- pity which is its opposite, and the true source of all real justice and charity....Envy, although it is a reprehensible feeling, still admits of some excuse, and is, in general, a very human quality; whereas the delight in mischief is diabolical, and its taunts are the laughter of hell. [Parerga and Paralipomena, Saunders, tr.]
Nietzsche thinks Schopenhauer is wrong:
Harmlessness of malice. Malice does not aim at the suffering of the other in and of itself, but rather at our own enjoyment, for example, a feeling of revenge or a strong nervous excitement.
Every instance of teasing shows that it gives us pleasure to release our power on the other person and experience an enjoyable feeling of superiority. Is the immoral thing about it, then, to have pleasure on the basis of other people's unpleasure? Is Schadenfreude devilish, as Schopenhauer says? Now, in nature, we take pleasure in breaking up twigs, loosening stones, fighting with wild animals, in order to gain awareness of our own strength. Is the knowledge, then, that another person is suffering because of us supposed to make immoral the same thing about which we otherwise feel no responsibility? But if one did not have this knowledge, one would not have that pleasure in his own superiority, which can be discovered only in the suffering of the other, in teasing, for example. All joy in oneself is neither good nor bad; where should the determination come from that to have pleasure in oneself one may not cause unpleasure in others? Solely from the point of view of advantage, that is, from consideration of the consequences, of possible unpleasure, when the injured party or the state representing him leads us to expect requital and revenge; this alone can have been the original basis for denying oneself these actions. [Human, All Too Human]
Those are the only significant explicit discussions I can think of. Aquinas does, however, touch on the issue indirectly in discussing the sin of hatred, which involves desiring and taking pleasure in another's misfortune. It also comes up in his discussions of the vice of savagery, which we exhibit when, instead of wanting people punished only according to what they deserve, we try to punish them simply in order to punish them. (The particular punishment involved in the case Chris is considering would probably be what Aquinas calls the punishment of ignonimy, in which one decreases the good name or reputation, or increases the bad name or reptuation, of someone in response to their deeds.)