Environment #1: grill surface. Cheese did not melt. Cheese turned slightly brown. No noticeable temperature increase on the side away from the flames.
Environment #2: coal surface. Cheese sat on the coals for several minutes with no visible reaction. Eventually cheese turned brown and hard. After about ten minutes, cheese was black and still not melted.
Environment #3: Rock with butane torch. Torch reaches average temperatures of 1500 degrees Fahrenheit (815 degrees Celcius). Cheese turned black where flame was applied; black marks did not transfer to the other side of the slice and temperature was not markedly affected except at the center of the flame application. Cheese did not melt.
For the last case, we also tested some "real" American cheese (as opposed to the "Platt" American cheese) and some unidentified cheese supplied by RyanRiegel. Both real cheeses acquired a sheen of fat immediately upon flame application; shortly thereafter the cheeses melted and bubbled slightly.