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What good would that do? So the coolant in your radiator will cool off a bit, it won't cool the engine because the water pump isn't circulating coolant. The one time my fans stayed on as you describe, I came back to a dead battery

 

heh thanks, i was just making sure i didn't have a problem that would snowball

 

Thirdgen fans unless modified go on and off with the key. The heat increase you see only lasts about 10 min or so then the block will start to cool. Some cars will still run the fan when it is off, but it is generally the all aluminum engines where you see it the most.