Is it the 528e "eta" engine?
I had a friend with the same car/engine and the same problem. Turned out to be a warped cylinder head. Any sign of that? Oil/coolant mixing etc? BMW indicated when he was getting diagnosis that many of the eta engines had similar problems. Of course, he was SO FAR out of warranty that admiting it was harmless for them. Unlike MB dealers:
When shopping for his 450SL, Dad saw a nice looking 1982 380SL at a dealer. Pulling the cover, he found a single row chain. Run away!! Well, the dealer flatly denied any problems with single row chains in that car.
1998 C230 "Black Betty"