Whether a thermostat is required depends on a number of issues:
1. Is you car computer controlled? If no, see #2. If yes, then you need the engine to reach the proper temperature so the engine management system leans out the fuel mixture.
2. Is the climate in your area cold? If no, see #3. If yes, then having a thermostat helps the engine to get rid of deposits that can cause sludge to form in the crankcase.
3. Take an old thermostat and removethe temperature sensing element, the spring and so on so that you end up with a disk of metal with a hole in the middle. Put the disk in the thermostat housing just like it was a thermostat. It will slow the flow of coolant through the system to allow the cooling system to do its job.