The amount of heat the radiator dissipates is proportional to the difference in temperatures of the water and the ambient air, which is why a water cooling system will reach a stable temperature... it's the equilibrium point, where the amount of heat dissipated by the radiator equals the amount generated by the CPU, and it depends on the amount of heat being produced by the CPU, and the temperature of the outside air. (assuming the fan speed stays the same)
However, the job of a thermostat in a car is to allow the engine to heat up.
http://auto.howstuffworks.com/question248.htm
a car's thermostat stays OPEN above a certain temperature, so it allows constant flow when the temperature is above that level, and allows no flow when the temp is below. if it was intended to cool water to a certain temp before releasing it, then it would have to work the opposite way (open when cooler than that temp, closed when hotter) This differs from a computer water cooling system in that an engine is supposed to be at a certain operating temp, and a computer must just be as cool as possible... but the point is, the coolant should be circulating whenever the engine is too hot, not sitting in the radiator. The hotter the radiator water is, the faster heat is removed, so allowing radiator water to be cooler than engine water would not make things cool faster.
Look at your description; you're contradicting yourself. what happens if the water in the engine AND the water in the radiator are above the thermostat temp? it stays wide open until the temperature falls below its set temp. having the water in continuous flow removes the most heat... the thermostat is making sure the temperature doesn't go BELOW its set temp, not above... when the temp is above, it's the radiator's job to get it back down.
if what you say is true, that allowing continous flow doesn't remove enough heat, then the engine would overheat if the radiator water and engine water were hotter than the thermostat set temp (it would never close, so you'd have continuous flow)
also:
"Yes, But it takes more energy to go faster so it produces more heat."
I think that's completely irrelevant. The amount of energy it takes to pump coolant through a cooling system is just a drop in a bucket compared to the amount of energy being consumed by the device generating the heat. not to mention, water pumps generally do not produce significant heat. The water pump I had when water cooling my computer was warm to the touch, never hot. even going to a higher-flow pump would still produce an insignificant heat increase compared to the heat of the processor.
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