Versorgungskreis der Heizung unterbrochen

A break in the power feed to a heating element rather than in the element itself, and it is worth separating because the module cannot tell the two apart from where it sits — it commands heat, sees no current, and reports the circuit. The element may be in perfect condition.

Heater circuits carry unusually high current, and that shapes where they fail. An intake air heater or a heated catalyst draws tens of amps, so the failure points are the ones that carry it: a corroded ring terminal, a relay with pitted contacts, a fusible link, a crimp that has annealed with heat cycling. These are joints rather than wires, and a continuity test made with a meter's tiny test current will happily pass a joint that collapses under load.

So test it under load or not at all. Measure voltage drop across the connection with the circuit commanded on; a joint that reads zero ohms cold and drops several volts hot is the classic finding here. Cold weather makes it appear and warm weather hides it, because these circuits only energise when the temperature is low enough to ask for them.