Hot Dog a la Potato

Preheat the oven to 350 degrees F (175 degrees C).
Slit hot dogs lengthwise down the center, but do not cut in half. Spread them open, and place them in a 9x9 inch square baking dish. Pile an equal amount of the mashed potatoes onto each hot dog.
Bake for 10 minutes in the preheated oven. Turn the oven off, and remove the dish of hot dogs. Place one slice of cheese onto each one, and return them to the oven until the cheese has melted.