AFAIK dogs "sweat" through their mouths only.. panting is the only way they have of cooling their bodies down. Essentially, their mouths, throat and lungs are a ventilation system distributing the cold air into their cores. It's why you have to make sure they have water on hot days also. They need to intake cold things to cool themselves off. They exhale the heat their blood has captured as water vapor as it passes through their lungs. We do the same thing through our skin.

I am not a vet however.