Not sure if your car has the AIR pump or not, the AIR pump only runs a couple minute upon cold start-up. Next time you start up on a cold engine, get out and look in the engine bay and watch the electro-clutch pulleys (if AIR pump equipped, you'd have two one for A/C the other for the pump). Could be the AIR pump is noisy or needs a new belt.
'73 280SEL 4.5 (9/72)- RIP
Only 8,173 units built from 5/71 thru 11/72
'02 CLK320 Cabriolet - wifey's mid-life crisis
2012 VW Jetta Sportwagon TDI...at least its a diesel
Non illegitemae carborundum.