My E36 M3 has recently had problems with the Climate Control system (intermittent shut down, settings get stuck, etc.). A little online research turned up this excellent page: BMW E36: Repairing the Climate Control Computer. The basic idea is that a capacitor fails inside and the computer has problems getting enough power, so it freaks out, doesn't respond, and generally annoys you.

If the Climate Control system in your E36 is having problems, you've got three options:

1. Get a dealer to fix it for you (probably $400 to $600)
   
2. Order a replacement Climate Control system and swap the old / new units yourself ($368 for new system, $221 rebuilt)
   
3. Try to fix the problem yourself (about $1)
   

I chose option #3, with option #2 as my backup plan.

After a little bit of struggling to get the CC computer removed my car, I took it over to the work bench. I found a replacement 0.47uF capacitor (tantalum) at Fry's for $1.29, and did a poor job of soldering it onto the board. It was so poor, in fact, that I was nervous I hadn't made the original problem any better, perhaps making things worse. Who knows? To my suprise, when I reassembled everything and re-installed inside the car, the Climate Control system worked beautifully! Total time spent: about 2 hours.

If you go with option #2 (either because you just want to swap the units, or you tried to repair it without success) you can order a replacement Climate Control system (OEM part made by BMW) from Pelican Parts for $368 (part # 64-11-8-378-466-M9) or a rebuilt unit (rebuilt by Programa) for $221 (part # 64-11-8-378-466-M250).

I have no idea what your dealer would charge for the 10-20 minutes it takes to remove the old unit and put a new one in, but my guess is "a lot", so it's probably a good idea to try to swap the units yourself. I've heard it's around $400 to $600, but who knows, your dealer might be higher or lower than that.

Note #1: From what I can see, the fix originated from "hoanboy" on bimmerforums. First here, and then later here. hoanboy, where- and whoever the hell you are, I owe ya one... :)

Note #2: If you decide to tackle the fix yourself, be aware that your car may turn the heater on automatically if you drive around without a Climate Control system installed (say, if you started working on it, but wanted to drive before you were finished). Once the engine warms up, you'd better hope you've reached your destination, because the heater will be HOT.