Overheating will cause damage to the engine and will also burn a thermostat throughout. A proper thermostat is in the engine to control heat, which occurs from the combustion of the fuel and does not add heat to the engine. If the air is not bled from the system the Fail-Safe thermostat can prematurely go in to the locked open position causing the part not to work.
The thermostat can be tested by boiling it in plain water for approximately 3 to 5 minutes, if the thermostat does not open, then it must have been damaged by the overheating. Installing a new Fail-Safe thermostat is fairly quick and easy, but always make sure to match the correct pressure cap to the correct thermostat to keep the correct pressure and temperature throughout the engine.