My friend borrowed my car for a week and he told me that he was at a stop light and the temp gauge rose and the car turned off. He waited 5 minutes and it turned on. He also mentioned that the fan stays on a while after the car is off and then powers off.

Is this a problem with my thermostat?

 

You need to diagnose the cause of the temperature increase. This could be caused by an inoperative fan(s), leaking cylinder head gasket, worn water pump impeller, clogged cooling system, malfunctioning gauge combined with a separate stalling issue, or faulty ECT and temp sending unit, low or contaminated coolant or a myriad of other things.

It could be caused by a thermostat. But without diagnosing the problem your guess would be as good as anyone elses.

 

I will drive it tomorrow and post back here.

 

if it stays on after the car is turned off only for a min or so thats normal and nothing to worry about, if it is on and will not shut off the relay is likely stuck (happened to me). the relays for the fans hang near the left side (drivers) of the engine bay right next to the AC fan