Fan running when car is off

The other day our 01 Durango's fan kept running after the car was turned off. Some one told me that when it's really hot out (which it was that day) that the fan would continue to cool the engine for a little while with the car off. So I was inside for about an hour and came back outside and the car wouldn't start. I had the battery and alternator checked but both were fine. Is it possible that the fan's sensor just stuck that one time and killed the battery or is it something more serious? It hasn't happened again (yet) and this was about 2 to 3 weeks ago.

Check relay

This just happened to me. It is not suppose to run with the ignition off. Mine turned out to be the fan relay in the power distribution box under the hood.

Check relay

2000 5.9 When does the electric cooling fan kick on and what makes it kick on? Never had this one kick on, yet. Thanks Z/