We have a 2002 Beemer, 325i with 80,000 miles. When cold, the car makes a soft whistling/whining noise. When very cold (as in, it’s been sitting for 8+ hours in cold weather), it can get fairly loud but it’s mostly distracting. Yes, the pitch goes up and down somewhat in time to the transmission changing gears but, it seems to go away when the engine warms up. Letting up on the gas doesn’t seem to affect the sound.
Is this a belt or is it the transmission? Or what?
By experience I have found a whining noise comming from the center support for the driveshaft,the intensity of the noise does vary with speed.
A second possibility (one that doesn’t seem as likely) is the crankcase vent valve (located under the intake manifold, a real problem to get to)they will whistle when ruptured,usually accompanied by a 'check engine" light.
A whistle that goes up and down with the changing gears rather than vehicle speed must be something upstream of the transmission.
I vote vacuum leak. Since it seems to be very temperature sensitive, I vote intake manifold vacuum leak as the first guess.
The test for that is to take a wrench and see if you can get a quarter turn on the bolts that hold the intake manifold to the head (without abusing the bolts). If the noise changes, that is the culprit. Not hard or expensive to fix.