I am not familiar with this particular model, but I suspect that it is very similar to the 124 cars.
The problem is likely to be in the pushbutton control unit. It is very common for these units to be fixed by heating the solder joints. Many times a cold solder joint is the culprit.
Also, the CD sold by merecedesshop will contain the needed troubleshooting information.
If it comes down to replacing the pushbutton unit, make sure you pay attention to the information that comes with it. There will be several checks to make, as outlined in the instructions that come with the unit. Check the Aux. water pump, and the heater control valve to ensure that the new unit is not overloaded causing a followup failure.
'84 Euro 240D, 516K miles
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'81 300D Daughter's Car
Over 800,000 miles in