Turning the heat on doesn't do anything for burping air out of the system, so forget about roasting yourself in summer time.
Thermostat has nothing to do with fan activation. The temp sensor detects hot water independently of thermostat operation. Thermostat only exists to allow cooled water from radiator to enter the engine block.
There is a strong possibility of trapped air within the system. If you saw the white smoke coming out of the tailpipes, your engine has a blown head gasket and may already be ruined and need of a rebuild. If the white smoke came from under the hood, there's a chance that boiling/overflowed coolant simply leaked onto something hot like an exhaust manifold.
Chasing any remaining air out of the coolant system should be the current focus. Taking the car to a shop with a professional OBD Sanner to run a test of the coolant fan should also be a high priority.
