Will, you'll have to forgive me as I'm not particularly technical when it comes to engines.
However, I had an issue last year that was similar although not the same that seemed to be affected by temperature. When my car was warm even if it had not been run (i.e. it was summer and it had been in the garage for weeks inside an air chamber, when ever I started it the engine management light would come on.
This happened a number of times. I had it into a number of garages (Morgan dealers and non-Morgan dealers). All reset the engine management but none could find an issue.
One garage (non Morgan) however offered a very plausible explanation. Apparently the BMW engines in these cars have a fan in the base of the coolant pump (I believe - pump was mentioned!!). The fan is known to fall off and as a result the coolant heats far too quickly. The fix is to have the fan reseated. If this happened again on my car I was going to have this investigated as my brother in law has a BMW, he was having simialr issues and when I told him this he had it checked out and that was his issue.
Luckily it has not happened since however I am expecting it to given the recent warm weather and the fact the car's been holed up in an air chamber.
Worth pointing out also that my car did stall twice and I had difficulty starting it. Again, not too different to your issue.
Hope for you it's the key/immobiliser mind - cheaper!!
Robin
