That's some good troubleshooting, especially adding the heater.
i would guess that there is a ceramic capacitor (C227, C229, C231) that is leaking as the temperature goes up. i chased something like this in a Volvo fuel injection computer years ago.
Maybe you can repeat this and then use a can of cold-spray with a small tube tip to aim it at those parts one at a time to find the culprit. And check this on the resistors in the voltage divider if it is not a bad cap.
Good luck and let us know what you find.