Actually, I think the opposite would happen. Your engine would never warm up! I have never tried this personally, however. What a lot of people don't realize is the water pump impeller is more efficient when operating with "head pressure". If you remove the thermostat, you will remove the major flow restriction in the cooling system, and the pump will operate without any significant head pressure. This becomes a problem when you rev up the motor, because the pump will start to "cavitate". Cavitating is when air bubbles form on the trailing edge of the impellers, reducing the efficiency of the pump.
In other words, don't remove the thermostat!