'07 Saturn Aura radiator fan running

I own a '07 Saturn Aura XR that has 155K miles on it. A week ago it started doing something strange. The issue I'm experiencing only happens about 60% of the time. What I've noticed is this - after I turn off the engine and remove the key, the radiator fan continues to run for about 3 to 4 minutes. Sometimes, just before shutting off the car, I'll notice that the temperature gauge is pointed higher then usual. I'm worried that one of these times the fan will not shut off and I'll come out to a dead battery. Luckily, this hasn't happened yet. So far I've noticed that the fan will shut off a few minutes after turning off the engine. And, like I said, it doesn't do this every time I shut off the car. Does anyone have any suggestions as to why the radiator fan continues to run even after turning the car off and the key removed? Thanks so much for the input!!