Henning, if the "black cylinder" is shown after openeing the cover byside and after removing the "Mischschacht", then this should be a Thermostat / thermo switch S1.

On, and off, in my understanding, at the edge of 80 degrees Celsius says the manual of the CLS 300.
As far as I know, the cables there function as a Widerstand, whats the english name, resistator ?
From my diagram of the CLS 300 they must have a length of 80mm .

I will offer the complete documents to the forum, step by step, please have some patience, I now have to work a bitt.
To be continued,
Ritchie