the best way to warm up an engine is put a light load on it (drive the car, but don't redline, shift early). really. it's better for it and it will warm up faster. you'll get better overall gas mileage, too.
it sounds like you could have a thermostat that is stuck open, causing the coolant to circulate before the engine is up to operating temp.
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Shawn
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The answer to your question is sqrt(pi)