Hello Carsten. If you are confident that you have used a known-good quality replacement battery, then I would ask where is the excess heat on your device?
There are 4 thermistors on the logic board (forehead, RCAM, Baseband & CPU) so if anyone of those areas detects excess heat, it will send you that error message. So wherever the heat is, that is probably where the problem is. It is unlikely that the thermistors themselves have failed although it is not impossible. More than likely, there is high current going through one of those areas due to a partial or full short caused by a bad component or module.
To eliminate any issues with the camera or front screen (forehead), remove the logic board and connect only the charge port and battery and see if iTunes sees the device. Then progressively add the screen (no fcam), home button, fcam, rcam etc until the message shows up. If it is in the baseband or or CPU area, the message will appear quickly.
Your problem will either be modular (i.e. camera) or logic board.