It has been said by someone smarter than me that the vast majority of engine wear occurs shortly after startup until the engine reaches its designed temperature.
The termostat in the closed position greatly reduces wear to the engine by reducing the amount of time that the engine is below the designed operating temperature.
Running an engine without a thermostat will cause undue wear everytime you start a cold engine. Undue wear is damage.
If your engine runs too hot with a thermostat, you need to determine what is wrong with your cooling system or your engine which it causing it to overheat.
