Tune up before decarbonizing
Yes, I totally agree with Darkhorse that you should check other things first before decarbonizing. In my case, the e34 just had a complete tune up, brand new injectors (X6) installed, and a new thermostat. Also, for good measure, the motor control unit (computer) had to be replaced because the output signal was not quite right. The air mass box was okay, as was the O2 sensor. About the only other thing we didn't check, and that is sometimes associated with cold weather start problems, is the cam position sensor. After these repairs and checks, there was still a cold starting problem and no problems once the engine warmed up, so my mechanic suggested sending it out for decarbonization. And as I stated earlier, it helped a lot. In my amateur search of the web, cold start problems can also be related to the spark coils (oil can seep into them if there is an oil leak from the top end). Some earlier model cars also had some kind of a cold start sensor or relay of some kind (ECT sensor??) but I didn't pay attention to it because that part didn't apply to my model. Good luck!