Mini Cooper S

I have a Mini Cooper S 2002 with 31000 miles on the clock. Recently, upon switching the engine off, the fan has started to come on and continues to whizz away for a good 15 minutes before the fan cuts off. Yesterday, the temperature guage went right up whilst trying to park - and then the fan kicked in again. It seems to be ok whilst driving normally and the temperature guage sits somewhere in the middle. I am a bit scared to drive it now in case I am causing more damage and don't really want a big repair bill. Please advise. Thank you.