Hannah Keyser writes How Do Cats Cool Themselves Off? (‘Here’s a hint: It’s not by sweating through their paws’):
Conduction allows cats to cool themselves off or warm themselves up via contact with objects of a different temperature. This is why you can often find your cat seeking out cool kitchen or bathroom tiles on a hot day. But this works for a dog or a person, too. What about when that’s just not enough?
It’s a misconception that cats sweat through their paws to cool themselves off. As summer wears on you might see moist paw prints, but as veterinarian Kimberly May told The Washington Post, “any secretions there or from their nose, mouth, or tongue are not for sweating; they’re for protection and moisture and are insufficient to cool the blood.”
Instead, cats recreate the sweating process—which works to cool humans via evaporation—by grooming themselves regularly. The saliva from their tongues acts like sweat that cools their body when it evaporates—which is why you can also help cool your cat down by using a damp washcloth to lightly wet their fur. In extreme weather, cats will also pant, but unlike dogs who pant regularly to keep themselves cool, a panting cat is a sign of more dangerous over-heating or other serious disease.