Like I said in the COC2 thread, it probably comes down to the amount of skin exposed and if they follow Earth animal equivalents. Fur and hair tend to trap sweat and can be a disadvantage in the wrong situation. So by that I mean that Humans use sweat as a means of thermoregulation through evaporation. Sweat forms on the skin and through evaporation cools the body. Sweat that is unable to readily evaporate (as in its caught in hair) carries various concerns, the least of which is that sweat is a highly saline solution, the salt of which can have a damaging effect on hair or fur.
So keeping that in mind, a quick look at the more commonly seen species in the galaxy can tell us something. Just a couple of caveats, though. 1) - I'm discounting reptilian, birdlike, insectile and piscine races. 2) - I'm discounting races endemic to Ice worlds like Uveto. One common survival phrase in Arctic conditions is "You sweat, you die". Sweating is dangerous in those conditions. 3) - I'm also covering some of the more human looking races, for the sake of completion. 4) - I'm not a xenobiologist, so most of this is just educated guesswork.
Ausar - Despite being more canine, the sheer amount of skin tells us that the desert dwelling Ausar probably do have sweat glands. That said, given the amount of hair on their bodies, I can't imagine their sweat glands would be as efficient as a human's, so they most likely combine that with panting.
Dzaan - Probably similar to humans.
Gabilani - Probably do possess sweat glands, due to originally living on Tarkus.
Kaithrit - Given that Rosha is a slightly-warmer-than-Earth planet, with large grasslands and forests dominating much of the surface and the fact that Kaithrit aren't completely covered in fur, they probably do possess sweat glands.
Kui-tan - Given the amount of fur, they most likely sweat through their hands, much like raccoons do.
Laquines - Probably cool through panting, like rabbits and dogs.
Simii - Given they're descended from Terran primates, yeah, they probably do sweat.
Thraggans - Evolved on a hot world, yeah, probably sweat.