An '85 500SE with a vent selector dial has two cabin thermostat valves rather than a monovalve on cars of that vintage with ACC. Find the valves and determine if they're getting a steady ground signal along with constant +12V to close the valves. If not, there's a problem in the signal to cut off heat. If the signal is good, you probably need new cartridges or new valves if cartridges aren't available.

The stiff vent selection dial is unrelated to temperature control. There's a cable in a sheath of 'positionable' rigid sections between the dial and the air box just behind it. Either the cable is binding or the levers and flaps it moves are binding. Maybe something fell into the defrost vents and is preventing proper flap movement.

Sixto
87 300D