I had the same problem - quite common on the blogs from looking.
Every time I turned the car off the fan cut in - over time got louder and lasted for longer.
If it goes on too long it drains the battery so you are right to unplug it ( Mini mechanic showed me how ).
I had to get a new fan fitted - wasn't very happy as I only have 16K on the clock but it's all fine and dandy now.
Expensive to fit as they have to take the whole front of the car off to get at it apparently - not sure if covered on warranty but I had a leaking roof in 3 times on warranty and in the end got a new roof and wasn't charged so I would like to think so. Got a deal on this so don't know what the dealer would charge sorry
