I thought they do, through their tongue. It’s cats that can’t sweat; that’s why they will have a quick burst of speed and then stop. Mine keeps looking for a cool paving slab in the shade to lie on. I wouldn’t want to wear a fur coat in this weather, although I once had a mate who was very hirsute. If he was in a white shirt it looked like he had a black vest underneath. Ugh! Puts most women right off..I don't really think you should leave a dog in a car in hot weather under any circumstances. Dogs can't sweat.
Cats sweat from the pads on their paws. Also, licking their bodies and letting the saliva evaporate simulates sweating.
http://www.petsadviser.com/pet-health/cats-sweat-through-their-paws/