Not a good idea. The whole purpose of maintaining a temperature in the 180 degree range is to assist with combustion. If you'll notice, as a car warms up it goes through a warm-up routine in which the fuel is enriched to overcome the inconsistencies in the combustion chamber. Once the motor gets up to a set temperature the warm-up setting is disabled and the car performs better and more efficiently. So if you remove the thermostat, depending on how efficient your radiator/fan assembly is you may never find yourself in the efficient stages.
Can it be done? Sure. Should it be done? I think you know the answer to that question.