I am having a terrible time with the heating system which does not respond to the temperature settings.

Well put. I've owned a '80 300SD since new and offer this suggestion:

The DEF mode should override the cold engine lock out and may override vacuum leaks so try that before signing onto these heavy $$.

Scrap this climate control system for it does not control the interior climate!

There's a US$699 digital retrofit system that replaces all this old junk; it's sold by PerformanceProducts.com  p/n 83-500

Back to your car's problem. There's a logic board called an "amplifier" that's located behind the glove box (remove it to access the black cigarette pack sized component with wires attached to its base). The board drys out over time and its solder joints crack causing bizarre actions by the climate control. Rebuilt "amplifiers" can be had for about US$100.

Then there's the cursed "servo" under the hood - that mushroom shaped valve body on the right side. Rebuilt servos cost about US$500, are too often flaky, and need to be returned for yet another servo (that you get to install).

So you are at a cross roads, pay $699 and fix it or (maybe) pay less and patch the old junk.

My '80 is overdue for an amplifier and a servo so I'm going to go the retrofit route but retain the old (still working) parts for now and hopefully sell them as cores after the new system has proven itself.

The climate control is very comfortable when it works properly so it's worth some time and effort if the car's overall condition justifies the $$ and time.