If the car has the M104 engine in it - the noise could be motor oil running through an oil tube that is too small to handle the cold, viscous oil quietly. This has been documented before and it won't cause any damage. I'm not as technical as other members here but I do remember this problem as I hear it all the time in the winter with my '94 M104. It goes away after about 4-5 minutes? What year is your car and how many miles?

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dtf
1994 E320 Wagon (Died @ 308,669 miles)
1995 E300 Diesel (228,000)
1999 E300 Turbodiesel ( died @ 255,000)
2006 Toyota Tundra SR5 AC 4X4 (115,000 miles) rusted frame - sold to chop shop
2011 Audi A4 Avant (165,000 miles) Seized engine - donated to Salvation Army
BMW 330 xi 6 speed manual (175,034 miles)
2014 E350 4Matic Wagon 128,000 miles
2018 Dodge Ram 21,000 miles