I've had my BMW specialist do a check using, I presume, all the latest BMW stuff. He couldn't find anything.
the most recent test was using Bosch diagnostic equipment, I think. Apparently it is pretty good generally, but will not cover the sensors. Does that sound right?
The rising 'smoke' looks more like steam (although it is not water vapour) and it does not occur all the time. As far as I am aware there is no leak or blockage in the exhaust.
As always the symptoms do not occur when the diagnostic test is being carried out.