03 E46 belt problem or ... ?
 

I recorded the noise today on the following youtube video:
http://youtu.be/_nc8Kn8zSs4
2003 E46 325I. Only with a cold engine, the noise will appear and stay for approx. 5 mins. I can push the engine to 5000 rpm, and the noise will also be gone. Somebody help! Is this a belt problem?

Probably an idler or deflection pulley.
Get the belt off and spin every pulley and appliance by hand to see which ones feel beat.
Replace whatever is wrong before you drive the car any more. You don't know when your next mile could be bearing failure, and cause significant engine damage.

You came here because we know more than you do. Heed this advice.

Thank you! I have been driven this car in this condition for at least two weeks already....

Gonna continue to drive it now?

I will have it checked at my earliest convenience. The strange thing is that the noise has disappeared for the past two days.

Calm before the storm.

Think about it: Those pulleys rotate at 2X engine speed.