1st, try turning on the Air Conditioning. All cars run the fan full time when the air is on. If the fan runs with the air on, you know the fan motor is good. And it's probably the fan temp sensor.
If it doesnt run with the air on, test for voltage at the fan. If you have power there, the fan motor is bad. If there isnt voltage, and the fuse is good, then it's the temp sensor, a short or an open circuit.
It's not the thermostat if you are cool while moving. It's very common to have a bad temp sensor though. I suspect that more than anything.
If the fan runs while the air is on, drive it with the air on until you find the problem. That way you wont damage the motor. Just adjust the heater temp up if it's cold in the morning, so you dont freeze your ass off.
If you need more advise e-mail me. We can get you fixed up pretty easily unless it's a wierd problem.