Head gasket = water in oil. Look at your dip stick

 

Temperature sensor in the engine DOES NOT "tell the thermostat how to operate". The temperature sensor provides a measurement for the fuel-injection system. The thermostat operates by itself to open & close the flow of coolant to the radiator.

 

If engine was in good condition before overheating, stick w/ your engine. A used engine can bring additional problems. A leaking HG is not a huge issue to resolve.

good luck