Verb (1)

Middle English distempren, distemperen "(in medieval physiology) to upset the proper balance of the humors, (of the body) be upset by improper balance of the humors, be diseased, (of a person) be indisposed, anger, (in medicine) to blend (two ingredients), dissolve, dilute, moisten," borrowed from Anglo-French & Medieval Latin; Anglo-French destemprer, destemperer, destremper "to mix together (ingredients, colors), prepare (a potion), moisten, cleanse" (also continental Old & Middle French, "to soften, dilute"), borrowed from Medieval Latin distemperāre "to affect (climate, the body) by disproportionate mixture, mix, soak," going back to Late Latin, "to mix (with another liquid), temper, mix badly," from Latin dis- dis- + temperāre "to bring to a proper strength by mixing" — more at temper entry 2

Noun (1)

probably in part noun derivative of distemper entry 1, in part from dis- + temper entry 1

Noun (2)

probably borrowed (with conformation to distemper entry 2) from Middle French destrempre "pigment prepared by the distemper process," noun derivative of destremper "to soften, dilute, prepare by mixing or diluting (a drink, mortar)," going back to Old French destemprer — more at distemper entry 1

Verb (2)

derivative of distemper entry 3