My 2005 X5 4.4 non-sport behaves the same. A 2005 X5 sport I drove before buying this one did not have the issue and idled quieter. It is going back to the dealer next Wednesday on its third trip for final diagnosis and hopefully repair. The software was update the first trip, the computer settings and log were uploaded to BMW NA on the second trip and they have been analyzing it under "PUMA"?

I will let you know what I find out next week. I believe it is cold weather related since it seems to make the condition worse. My truck spent its first three years in West Palm Beach, FL so I do not know if the original owner observed the symptoms or not.