Quizzed my ever helpful service guy at Woodmans about this.
MINI do know about this, but it is NOT a fault. Therefore, there is no fix, because it isn't broken!
I was given a big technical reason as to why the fan goes off, but I was quite honest and said "so what does that mean in plain english?"

Now I am not technically minded, nor a memory man, but I shall recall what I can
There is a 'particulate filter' that occasionally needs cleaning out. I think it is near the exhaust. To clean out the particulates, the exhaust gases have to be higher than normal, to burn them out. The engine runs hotter and faster than it needs to, just to generate a hotter exhaust gas. To protect itself from overheating, the engine fan comes on, to keep the engine cool. This is what it is supposed to do - hence why it is not a fault.
MINI admit that some users may find it "incomprehensible", especially at the fact the fan may run in sub zero temperatures.
Again in plain language, "live with it"
I think we are all going to have to accept it as a quirk of a Cooper D
