When dogs pant they inhale through the nose and exhale through the mouth how does this provide a cooling mechanism?

Through the nasal cavity a major a mount of vapor is released during inspiration and expiration as well.

This vapor is warm and during expiration its released into the environment.

During inspiration fresh air gets into the nasopharyngeal cavity and cools down the animal.

This "used" air gets warm and leaves the nasal cavity via expiration