I have been reading this thread because today on my way home the engine cut out on my '97 740i. I coasted through the intersection and pulled over to the side of the road. I saw some smoke under the hood and smelled something burning. I opened the hood and saw some smoke coming from the front of the engine cover. While looking I noticed a small flame starting. Instinctively, albeit stupidly, I looked at the small flame and blew it out.
I called my mechanic and he told me that, without looking at it, it sounds like the thermostat but he will look at it tomorrow and assess the damage. If I didn't blow out the flame, the car probably would have burned out. Well, let's see what happens. Hopefully, it's just the thermostat. The car has 74,000 miles on it and I was hoping to at least double that.