Hair/fur acts as insulation by trapping heat. The fan moves air across the fur and releases some of that trapped heat; plus if the dog is lucky, it will blow his ears back (back to that radiator theory) and help cool him all the more.
Ike, to this day, will bump his head into my arm, and then sticks his nose at the dashboard. That means "turn that air vent towards me, please" and his favorite place to sleep is in front of a fan so he doesn't have to pant to stay cool.
