Head gasket, perhaps..... pressurizing the cooling system with combustion gases. If that's what it is, it'll soon take the radiator along with it as the pressure splits open the radiator core or hoses.

It's also possible the thermostat is stuck partially closed (reason your heater works so well?).... if you're lucky, that's all it is. I'd first try replacing the radiator cap and thermostat and see what happens. It's cheaper to test, but for no more than they cost, you'll want them anyway if you have the radiator rodded or the head gasket replaced.

Frank