I have a 2002 MINI Cooper S the past when the temperature outside gets in the teen's my shifter will not move. Once I start and let it get a little warned up its fine. I have also noticed lately a whine on the driver side. Sounds like my cold air intake but louder. This also is only when I very first start after its sit over night.

 

Have you changed your transmission fluid?
I had this problem last year. My shifter would stick if it was 30 or below. Changed the fluid and haven't had the issue since.

As for the whining, I'm not sure.

 

Bet the trany oil was changed to something too thick...
Have heard of it happening before...same folks also reported lower mpg.
Fix...change to the "right" fluid....not just what folks say work...
Hopefully a bering was not destroyed from lack of lube...

 

I changed it back in the summer. My mechanic recommended Redline gear oil. It was 75w80

 

Redline MTL 75w80 should be good.
Could just be your cables binding a little when cold. Could remove the bottom cover (above exhaust) and inspect. The joints might just need a cleaning and lube.

 

Think that is the right stuff on the pre face lift cars...not 100% sure cause I have a newer car..folks do use the older spec oil with no LSD....
The 2005+ cars switched to a lighter oil, due to the possibility of a LSD...
I would research it a bit more to see if the redline is the right stuff..
Might have been one of the thicker mtl's like Royal purple that folks had cold weather issues with...
Edit..waymotorworks says (I think) redline mtl http://www.waymotorworks.com/redline-mtl.html

 

I'll look at the bottle when I get home tonight see which one it is.

 

I'll look when I get home tonight

 

If you changed your fluid, either it's too thick or it is your cables. The shifter cables have a boot on them that "protects" from crud. After awhile it becomes dry and allows moisture in that freezes when it gets cold.

 

Where are they located?

 

The cables are on the bottom of the gear shift assembly. You access access the cables from underneath the car. You probably need to un-bolt the exhaust to remove the cover and access the cables. Since your car is an 2002 and many things were different in that first year I may not have grabbed the correct diagram but it should be similar.

 

Looks correct I got on RealOem searched by my VIN diagram looks the same.

 

I had this happen last year with the beater miata I bought. The miata shifter goes straight down into the transmission so there are no cables or anything to freeze. The shifter would be frozen in whatever place it was in when I parked it the night before. After the car would warm up some I could unstick it and it would work fine from then on. I changed the trans fluid a few months ago and haven't had the issue yet this winter. I'd try changing the trans fluid since you probably need it anyways.

 

I checked the bottle to see what the fluid was I used when I changed it. Redline MT 75w 80 which is what it calls for to use I'm pretty sure. I'm going to the dealer to get the OEM fluid and try that see if that makes a difference. I got my Bentley's manual out last night to see about the shift cables you do have to remove part of the exhaust then the heat shield. I'll definitely be paying someone to do that.