1996 328i (160k miles) leaks oil during start-up when the engine is cold then stops when engine is warm.
I used to have that problem and it was the oil filter housing. Edit: Same year, same motor, more miles.
Cam Cover I have seen the cam cover leak when cold and after sitting for a few days. The leak would then stop after the engine warmed. Is the oil at the front or rear of the engine?
Best thing would be to work with the tracing method and follow it to its source. My guess is that it is probably a worn gasket that may become plyable when heat is applied, maybe? I cant think of any other scenario that might cause that. Warm oil is thinner than cold oil seems like it would make it leak more if it were a broken piece / "hole" P.S. if its a head gasket and you decide to pitch the car let me know! =)
You need to be more specific. I could give you every single oriface from which your motor can leak oil, but that would be silly. Tell us where you think it is leaking from and we can tell you what we think it is.