Man it's hot. Let's take the feet for a walk! So how does your dog sweat? All that hair surely doesn't allow sweat glands to function does it? And no! They don't sweat through their tongue either. It turns out, that dogs sweat from the pads of their feet, as it is one of the only places not covered by fur.
Paw
However, it IS true that dogs cool off by panting. It's just that they don't sweat from their tongues.