I will back off just a bit and say I am 95% sure that the hardware is indeed heating and causing these alarms, if that helps any.
Technically:
My conclusions are based on my educational EE and CS engineering background at a well respected educational institution along with career experience in both areas, coupled with the tear-down photos. Finally some other independent test results were supplied on a different forum that utilize more than just temperature readings, but the increase in ISO noise on dark frames as the temperature warnings go off, showing that there are indeed physical temperatures that can be matched to the warnings, those that conducted the tests just don't know the exact temperatures that make up the ranges.
There is indeed software involved that could help the situation. Better functional design and memory management can reduce the workload significantly. The fact that the next firmware update will allow folks to record in light raw format which shrinks file sizes down for video substantially (an option reserved so far for their cinema line) shows that Canon is trying to find ways to reduce the load on the camera.
Logically:
Ignoring all these other facts and my own eperiences, if it were just arbitrary limits, Canon would be able to address these concerns a bit easier. I am sure they don't want to open up options for recording reserved thus far for their cinema line. If it were arbitrary software limits that are causing all these issues, then I presume Canon engineered these with prior bodies as well (like the 5D4), but never implemented that code until now. That seems a bit odd. The most logical answer is that Canon packed so much into this body, both hardware and firmware, that the final product now has some issues that they have to deal with. The combined package with IBIS, deep learning, eye AF algorithms, dual gain amplifiers, and possibly even some NR in the low ISO raw files has created some combined software/hardware complications.
On Principle:
If people believe that Canon marketing and software teams all got together to figure out how to hobble this together and make all these issues apply with software, so that they could deal with the bad press on these two releases, only to save face later by "fixing" that code to eliminate these problems, then why would they even be looking at Canon gear, or support that kind of business model? Wouldn't they move on simply due to principle alone? Also, what would the goal be? To force people to NOT buy these two cameras and instead wait for some future R1 body to be announced at 3x the cost? That certainly wouldn't look like marketing genius, whose goal is to maintain or gain market share, correct?
Generally:
Now perhaps you are of the belief there are indeed high temperatures in the camera where different sensors are picking up on heat from the processor, ram, I/O channels, etc and the software has arbitrarily low limits that kick off these warnings and eventual shutoffs? Then yes, I can see that too, but the reason would be that Canon is looking to their bottom dollar on warranty repairs and replacements (and longevity hopefully), so they set these limits pretty low perhaps. What that means is that Canon, like Sony, will back off a bit and raise those limits to allow more recording time, but just a bit more. None of that changes the fact though that as soon as you turn on the camera, the clock starts ticking down on that video capability that you might want to utilize, and that is perhaps the largest issue at this point, coupled with the really lengthy cool-down period. 
