This is a 2010 Mini non-S with 108K.that I've had for a year and a half. I did a search but was unable to find one like this; on cold start I get a very brief whine or screech (sounds like a cat is caught in the fan) then it goes away. Never happens again until it sits over night. I have no other out of the ordinary noises. .

Any clues on where to look, yes, there are no cats under the hood.

 

when i had that issue (07s) it was one of the (2) water pumps, but i don't remember which. my mini was still under warranty when it happened, so the dealership replaced it. during my experience, initially the screech was short, then after some time the duration of squeal became longer and louder