I have the same/similar problem, with Heat is ON all the time , in my 87 300 D Turbo.
Need help. here is description and some facts so far:

The ACC unit died so I bought one on ebay and it seemed to work OK for a while.
Then The Heat Start coming ON and stayed on.
I have removed / eliminated the Aux. pump ( which was corroded to death) and put a pipe in the hoses . Hot water definitely flows through, hence all the HEAT.

I have checked the Mono Valve, It works fine, w/ 12Volts applied to it, shuts down the heat. Thats how I have be turning the heat off, by hot wiring the Movo Valve.

I checked the voltage to the Mono Valve , here are the Voltage Values:
Everything Off, Car, main Elect off: 0 Volts ( obviously)
Engine on, but ACC OFF: 6.1 Volts ( I think it should be 12 V)
Engine on, and ACC ON: 6.2 Volts , with any Temp wheel setting (max cold to Max hot)
By the way, when moving the Temp wheel setting (max cold to Max hot), I do hear a click within the ACC , but he Voltage to MonoValve does not change from 6.1 V DC.

So, sounds like either another bad ACC or something else like the Cabin Temp Sensor or What else? Need help here...
How do I check Cabin temp sensor?
or whatever else?
My 1987 300 D Turbo body is 124.133
I think my ACC part number is 124.830.18.85 ( It was some how discarded , when I bought a "similar" but not exact part number from ebay)
It is hard to find the exact part number ACC.
Can someone tell me what other ACC models would be compatible w/ my car?

Thank you all.