Dogs cannot sweat, so they cool themselves entirely by panting, tongue out, the only tool they have. It is the standard explanation for why a hot dog turns into a furry steam engine on a summer walk.
Panting is a dog's main way of shedding heat, but it is not the only one, and it is wrong to say dogs do not sweat at all. Dogs have sweat glands too, just not all over like us. They have merocrine glands in the pads of their paws, which is why a hot or anxious dog can leave damp little footprints on a smooth floor, and apocrine glands across the body that play more of a scent role than a cooling one. The reason panting does the heavy lifting is that a thick fur coat makes sweating through the skin nearly useless for cooling, so dogs evolved to dump heat by rapidly evaporating moisture off the tongue and airways instead. So the accurate version is: dogs cool mostly by panting, and a bit by sweating through their feet. Not 'dogs cannot sweat', which is one of those facts that is almost right and therefore especially sticky.