91 850 - Wont start when hot

I have a 1991 bmw 850 which runs fine when first started. When I arrive at a place say 20 miles away, switch off and wait for a short while, the car will not start. Turns over fine, but no spark, no fuel pump prime. After a varying amount of time (about an hour?) the car will suddenly spring into life as if nothing had happened! The immobiliser has been wired out, because I suspected this. I cannot find anyone with the relevant equipment to read the codes, as the protocol doesn't seem to be the same as any of the modern scanners, so I don't really know WHY there is no spark or fuel. Is it the EML or DMEs that control the spark / fuel, and what provides power to them? Anyone any ideas??
The fault seems to be worse when the weather is hot, indicating a "heat failure" of some component..........