From what I read before, the high idle at warm might be due to, I'm not even 80% sure, secondary air system. I just very vaguely remember that on top of my head.

Good Luck!

__________________
01' 3.0i E53 (M54) with 164,000 miles
07' 3.0si E83 (N52) with 134,000 miles
08' 3.0si E70 (N52) with 91,000 miles