i agree about the valve adjustment, I think they are just clutching at straws there.
Until you said they had done a full diagnostics check, I would have gone straight for the two thermistor sensors that feed into the ECU. One is the air temperature sensor in the air box, and the second is the cylinder head water temperature sensor. I don't know what they did but I would be looking at those sensors to see if their temperature readout in diagnostics was about right for cold air and a cold starting bike.
The next thermal thing is the egine thermostat. After starting and running, do you see the temperature gauge slowly climb up to about normal, or does it stay stuck around the cold mark on the gauge for quite a few miles?
Another thing to feedback, does the bike run rough when the engine is at normal temperature but you are riding in very cold air? If yes I think that is an intake thermistor/ECU problem.
I don't think they were there with the O2 sensor but they changed it anyway. When you cold start, the O2 sensor is locked out of the loop for about 3 minutes to allow time for its heaters to get the sensor hot. The ECU is giving a very rich fuel map and I would be surprised if you got cold start mixture problems.
The biggest problem cold starting these bikes is most likely to be flooding. Cold fuel does not atomize so well and it is very easy to flood the motor and get no start. When I cold start I NEVER twist the throttle when cranking. I give it maximum 3 cranks on the throttle stop and if it doesn't fire I leave it 5 or 10 minutes and try again. Before I learned my lesson on these bikes, I took plugs out after several cranking attempts and they were soaking wet with fuel. You could look at your plugs if you get into this state, because it will tell you if you have a fuelling problem or not.
Find out what version ECU is in your bike. There have been issues and various changes and warranty swap outs. Your bike may have these problems others have found which only show up in very cold air temperatures.
All the signs point to mixture fuelling, but weak spark could behave the same way. I assume you have no issues with the battery? Low temperature often comes with damp and moisture. Seeing where you are, I might also look at the plug leads. BMW have always used rubberised HT leads and they are quite expensive. Somebody here found a supplier who could make up silicone HT leads. Take off the left side plastic and run the motor in a dark garage. Look around the HT leads and poke them a bit with a plastic rod. If you see a blue glow jumping across the leads or to the frame, that is corona caused by insulation breakdown. That is spark energy lost and you most need it for cold starting.
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