I'm not sure that the heat is a problem, but the other outputs to check are the switchover valves that control the vacuum to the control elements.
The logical reason for all the heat from the system is that the monovalve is not being closed (allowing hot water into the heater core). The pushbutton does this by grounding the valve. Test the voltage at the two valve connections. One should be battery voltage and the other should be arouind 1v (the PBC doesn't pull the thing all the way to ground). Power on both sides means that the PBC isn't controlling. Power on one side and zero on the other side can mean an open circuit in the valve coil (also keeping it from functioning).
Bosch Master, ASE Master, L1
33 years MB technician