1. If BMW truly has no idea, then don't believe the dealers guess about an engine heater
2.if the car needs an engine heater to be able to to operate in the region into which BMW sold the car, then BMW must provide it for free.
3. there is a huge amount of data on your car that you/we dont have...initial codes, frequencey, test plans run, results, etc, etc, I used to have my SA document the codes, testplans and results- along with part replaced, etc- on my WOs. Many page documents. When I pressed for a lemon complaint on my 2010 with 32k miles, there really wasnt much discussion.
Keep it as simple as possible...but no simpler.