Should you run a car without a thermostat?

Absolutely not. You need to fix the actual problem. With no thermostat, the coolant flows with restraint and doesn't stay in the radiator long enough to cool properly. It can actually run hotter w/o a t-stat under certain condition.

That is a myth, I get by each summer with no thermostat, engine runs 10--15 degrees cooler. The 180 will be going back in soon but come next May, off with the thermstat once again. Engine warms up quick in summer heat and hold 170 to 180 while driving, perfect for my set up