The thermostat, as someone else just pointed out, acts as a restriction that limits the flow through the radiator. When you remove the thermostat it is possible for the water to pass through the radiator before it has had adequate time to lose its heat. In NASCAR they replace the thermostat with a needle valve affair that can be finely tuned to maintain the temperature they want BUT that engine operates in a small RPM range that remains fairly constant throughout the race and they have special procedures used during warm-up that saves the wear that one gets with an engine that does not have a thermostat.
Granted, it CAN work out that a particular engine/radiator combination can run just fine without a thermostat but that is the exception to the rule, NOT the norm. Modern cooling systems are carefully designed to maintain a constant operation temperature throughout all seasons and the thermostat is the heart and brain of that system. Engines run most efficiently at a particular temp and the ignition and fuel systems are also optimized to operate at those temperatures. Take out the thermostat and you have just thrown the whole system out of whack.
