Hell, might not even be a radiator problem. You might have a slight leak in the head gasket and getting a small amount of combustion gasses into the cooling system, which would DEFINITELY cause your radiator to overflow, and subsequently overheat once you lost a bunch of coolant. Race gas ain't fixing that problem.
But who knows, it might actually work. Switching to race gas (as Jerry pointed out above) will often effectively richen your jetting. If your overheating problem is caused by a lean condition, you might actually stumble upon an effective solution by accident. Of course, if that IS the case, re-jetting would be just as effective and a whole lot cheaper.