I'll throw this one out.
The default state of the monovalve is wide open. With the engine off, coolant is allowed in the heater core. If you start a warm engine, the heater core will continue to be warm for a while.
MB's solution in the W126 is to have an air path between the evaporator and the center vents that bypasses the heater core. There is an alternative path to the center vents downstream of the heatercore.
If the W124 system is comparable, then you might have a bad center vent flap actuator (the center vent flap is downstream of the heater core) allowing heated air to go to the center vents. Eventually the heater core cools down because the monovalve closes when the engine's running and the AC compressor is engaged.
The monovalve is closed in cooling modes, open in defrost mode and othewise cycles to modulate temperature. I suppose you can measure the duty cycle of the monovalve to test that it's working but I don't know what the correct frequencies should be for a given cabin-desired temp difference.