I have a 2007 Mazda6 with the 3.0L V6 that I have owned since new.
This (extraordinarily hot) summer I noticed for the first time that the radiator fan runs for 5-10 seconds after I turn the car off, even with the keys out of the ignition. Initially I thought this might be due to the extraordinary heat, but we've had a few cool days and I've continued to observe the behavior, even after short drives on which the engine is barely reaching its normal operating temperature. Now I can also hear it turning on shortly after the engine is started – something I don't remember hearing ever before (but also something I may not have noticed).
I had the coolant changed a few months ago. No signs of overheating in any condition.
My naive guess is that some temperature sensor has failed. Any tips on diagnosing or debugging the behavior?