Good points NurseMike. I had seen the stories on Popov and that was quite sobering.
I've seen some material from US Army research that shows heat illness to be a somewhat inflammatory response, not just a heat transfer problem, and that aligns with your post. The Army has found that heat stress is cumulative, and making it through the night after a hot day is no guarantee of surviving the next day's heat.
Like BacPacJac says, if I stay on top of things I can stay warm in the cold, but even if I do everything right I can't make a lethally hot environment cooler.