I have this exact issue. I thought it was related to the cams I'm running though. I just recently bought a 91 318is with a blown head gasket. So I replaced the motor with a VERY low mileage motor that had regrind cams (schrick specs). I have start issues exactly as described above for about 2-3 minutes then all is fine and dandy. Engine temp has no effect on the problem, just turning off the ignition and leaving it for more than a couple of minutes will trigger it.
I thought I needed a custom chip for the car to fix the issue, but maybe the problem is something else. Any help would be awesome, it's kind of annoying having to wait for the car to start idling properly before driving.