won't shift up when cold…

Today’s transmissions are nearly as much electronic as they are mechanical so I suspect that one of the sensors used by the transmission may have failed. First, I would get an OBD-II scanner and see if it might show you an error code that would lead you to the problem-causing sensor. Of course, the reading you get from the diagnostic scanner will be generic since the scanner will be set up for the “universal transmission.” A “universal transmission” is a generic device that covers every vehicle so despite the fact that you have a GM transmission under the hood, it is unlikely you will get more than a generalized error report.

Not to worry, though, because even if the report and error codes are generic, they still point at the area or areas where there are problems. If you want an exacting error printout then you will have to invest some heavy duty funding ($1,999 or so) to purchase a BMW=specific OBD-II scanner and current software update. If you plan to hang onto your BMW for a while then it might be a good idea to purchase a subscription to software updates because you may have to run other diagnostic scans to find out if there are other problems.

In the case of your BMW, I suspect that one of the temperature sensors on the coolant lines may be on the way out. Though it is only just starting up, it is throwing enough of an error across the engine to cause the poor early performance. It might be that a sensor/solenoid pair may be included in the error and if they are then you will have to replace the pair.

Indeed, the heat sensor in the transmission acts like other under-hood temperature sensors. Connected to a solenoid, the sensor waits until a specific temperature before it opens, allowing coolant to circulate through the transmission cooler. If the sensor fails and the solenoid that it fires fails for a few moments, then your transmission will act exactly as you describe. Let me know what happens, if you would?