I'd try the radiator cap before anything else. The heater core would not cause that to happen even if it were clogged it is not an important part of the cooling system. Also make sure to get all the air out an air bubble can slow movement causing it to heat up. Also do not remove the thermostat it is there for a reason, removing or altering it could cause the reverse to happen and you could actually move water through the radiator to fast for it to be cooled.
