Another slightly devil’s advocate type analysis...
Imagine an old fashioned electric bar heater in room of a house. There are three temperatures we could measure. The environmental (outside), the room and the heating element. There are clearly some relationships between these measurements. But not linear or simple ones. The temperature of the fire itself will rapidly increase but then stabilise - irrespective of the room or environmental temperatures. It is easy to imagine that the fire has a safety feature such that after X minutes at T degrees it shuts off. That shut off time is not proportional to the environmental (cf the fridge) or room (cf camera body) temperature. Neither of those temperatures has a significant effect on the temperature of the heating element of the fire.
Now, if the Canon API reported temperature is the “room” (possibly the camera body) that is clearly irrelevant to the critical “heater” (the sensor or CPU or part thereof?) temperature and would not, therefore, relate to the shut down. Of course, this doesn’t eliminate the possibility that the shut down might be simply on a timer and not contingent on any measured temperature - but I suggest that it might be based on a “time at temperature” model of some key component or part thereof. The latter view permits some variation with the timings which seem to be reported (if on a simple timer it would be expected that no variation would be observed).
If this type of analysis is correct then measuring temperatures or using reported temperatures doesn’t address the actual issue. The issue remains one of fundamentally abject design and/or manufacture or a totally bizarre business decision (and certainly offers absolutely no defence of Canon). Someone needs to get this camera into a physics lab and get to work on it... then send the findings to an “on the balance of probabilities” expert.