Trivia 2: as your reference says, the disease comes from the idea of not being properly balanced (not being well-tempered, like Bach's Clavier). On the paint, the Concise Oxford Dictionary of English Etymology says this:
"distemper 2 †mix with liquid, soak XIV; fig. dilute XVI; (f. the sb.) paint in distemper XIX. — OF. destemprer or late L. distemperāre soak, macerate, f. L. DIS- 1, 2 + temperāre mingle, qualify, TEMPER.
Hence (after OF. destrempe, mod. dé-) distemper sb. 2 method of painting on plaster XVII; whiting mixed with size and water used in this XIX. "
https://www.encyclopedia.com/plants-and-animals/zoology-and-...On Trivia 1: I can't think what it is! Please put me out of my misery when you think I've stewed for long enough.