Depends on how much skin is exposed, I suppose. And whether or not they required perspiration as a means of thermoregulation.
Humans have a larger number of sweat glands compared to other mammals, except for monkeys, the apes and horses. Perspiration, for us, is a rather efficient means of cooling down for us, especially compared to other animals like dogs, who pant.
So the likes of Tanuki probably sweat through their hands.
Lupines probably pant.
Minotaurs probably have to rely on respiration to keep themselves cool, as bovines don't have a good perspiration system.
Taeleer and Kitsune have enough exposed skin that they probably have sweat glands.