Just because it leaks (if it is leaking), doesn't mean it will overheat. You have other problems. Any nasty milky looking shit in the water? Are you adding antifreeze each time, or just water? The system needs antifreeze even in the Summer.
I'd do what's mentioned above since it's a cake job; swap the thermostat and make sure you get it full. You should be able to see water seeping out of the small hole on the underside of the pump if it needs replaced.
Big air bubble, clogged radiator, stuck stat, head gasket, pump are all possible. I assume this has a mechanical fan?