This is almost certainly a problem with the actual heater control unit (the thing that sits in the dash). It very likely has a bad solder point in. Temperature changes cause the metal inside the unit to expand and contract, and contact points can come loose or break over time. This was very common (and a known problem to BMW) in the mid to late 90s. Based on what you have already tried to fix the problem, this is pretty much the only thing left so I am very confident this is your problem.
I had a 1996 318i with the same problem, I replaced the dash unit with a refurbished one (knowledgeable techs take them apart and beef up the solder points).
I would suggest getting a replacement refurbished unit off ebay. This will be the quickest and most cost effective way to fix your problem. They are easy enough to swap out. Here are some links:
Or, you could send yours in to be fixed up:
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I don't think you will be able to fix the dash unit yourself, although if you are a proficient solderer you might be able to attempt it if you can find a step by step guide online. Try searching for E36 climate or E36 hvac and see if you get lucky.
You should, however, be able to swap out the unit if you buy a replacement one, that's easy enough - just a few clips to get the unit out, then one plug at the back.
Good luck and thanks again.
Oh okay, good to know.
You should be able to have that refunded by justanswer since you never had the second quesion answered. You probably have a positive balance in your account, which you can just request a refund for.
Thanks again and good luck. If you can't sort out how to request a refund on the site, just email them at email@example.com and they will take care of you.