I've been doing something similar all summer except on my gas grill. Better crispiness, bigger pizza, less oil, and of course, no heat in the kitchen.

Roll out dough (I like whole wheat) on a floured cutting board. Brush with olive oil and sprinkle w/corn meal if desired. Flip dough on to grill at around 500F. Cover and cook until crispy. Oil top side. Move dough back to cutting board with crispy side up. Place as many toppings as you want. Slide it back on the hot grill, cook until crispy.

It's a good cooking method if you like lots of sauce on the pizza.