My fan will stay on for about 2-3 minutes after I shut my car off. It didn't do it when I first bought it, but i'd say it's been doing it for about the last couple of years. It will come on regardless of outside temp, though it usually won't come on unless I've driven the car for more than 30 minutes. Might be a bad temp sensor, but it definitely will not harm anything.

 

Ive been through that with my accord. First check the fan relay in the fuse box. After that (and this is what fixed the problem in my car) change the auxilary fan switch. Once I replaced that, the fan never stayed on after I shut off the car. Keep an eye on your temp until you fix this. My car would try overheating everytime i was stuck in traffic. It causes the fan not to turn on when the car is running, but it will turn on when the car is shut off. Hint - If your temp stars going up, turn on your AC.