Please Help! x5 4.8is Whining Noise On Acceleration (cold weather related)

[BMW-x5-48is]

Guys, I have noticed last year during winter a small issue that I didn't take to heart - the problem does not exist in summertime when its warm outside. I can turn the car on and drive and no whining noise upon acceleration. When its really cold outside, the car, takes a good 40 minutes of driving at-least to warm up. When car is warmed up fully, the sound does not exist - but my drive to work is 25-35 minutes - and I run into the whining noise everyday once temp dips below 40F. Today when I started the car (29F outsdie) and start to drive it, there is a whining noise coming engine bay or what seems to be right under driver seat more towards engine bay as the RPM's go up. This happens in the 1st and 2nd gears once car is starting its day.. The whine is getting pretty bad as this winter approaches, last winter was barley noticeable... So I want to find problem & eliminate it - before we start getting these cold ass 15 or 20F days..

guys what could this be? did any of you experience this? someone recommended replace transfer case oil and drive for atleast 1k miles to see difference, others said, check engine belt & idler pully or replace them, others are saying to check timing chain guide.. I want to locate the problem more exact if possible..

Did any of you guys ever experience this whining noise in cold weather upon acceleration especially when using the Manual triptronic mode?? This is def COLD weather related because you dont hear the whine when its 70F outside - but the colder it gets - the more of a whine exisits especially if temps dip below 30F - if its between 20-30F the whine is annoying!! It does not have impact on performance, the car pulls good, but the whine gets worse as RPMS go up, and its when outside its cold, and car is cold.

This WHINING NOISE (almost like a supercharger) exists when:

1.) When car first starts its day in morning before its fully warmed up (which happens after an hour!)
2.) When its cold outside (35F and below - the colder it is - the worse of a whining sound). The sound can be compared almost to like a jet-engine when it powers up.

3.) The whining happens in 1st and 2nd gears as car accelerates up to 4K RPM and I shift (sound disperses on shift into 2nd) and once 2nd gear starts being used the sound becomes less loud, until it fades out once i switch to 3rd gear..
4.) When using triptronic (Manual) the sound is worst in 2-3RPM range once car warms up (after 40 minutes) sound is less and less - when using (D) the sound is NOT as noticeable - but thats because (d) shifts in lower RPM then I do when i use triptronic - i usually bring car up to 3-4k RPM when shifting and this whining noise builds up lounder and lounder as the RPMS climb (This is only when im driving!). When I rev the car in Park or N the whining sound does not exist - its only when car starts moving.

5.) The sound starts at 1000RPM and increases its whine up to 4k RPM disperses when shifting - comes back in 2nd gear from 1RPM to 4RPM again and in 3rd gear (once car is moving 40MPH or more) the sound goes away completly.

6.) Again this sound is dependent on the cold weather - the more cold outside it is - the more of a whineeeeeeeeing (jet engine like/supercharger like) sound I get... fking weird... didnt know I had a supercharger in this 4.8is..

I ruled out Generator because it was replaced and problem with whine still here. Ruled out power steering fluid because turning wheel or making a turn has no impact on whining sound and I did not notice any steering issues or fades. Did any of you guys experience this sound/issue?? I have a 2006 bmw x5 4.8is by the way..

Any help on this matter would be GREATLY, greatly!! appreciated.... as its annoying me to the max and I love my car..