Engine Cooling Fan Question

[Sunnysu]

I've just been reading one of the other posts and it has prompted me to ask:- Should the engine cooling fan on an early S1 stay on for a while after the engine has been switched off if it is hot?" The engine has overheated a couple of times during warmer weather. I have been told to leave the engine running to keep the fan running.

[Sunnysu]

There have been suspicions about the reliability of the thermostat as the engine temp has always been on the border of the red upper (boil) limit on the dial. The engine has only really boiled once and that was in June on an absolutely roasting day after a longish run.