Your premise that they are different problems with older and new phones is an assumption, and one not necessarily supported by any real evidence. Agreed it is somehow heat related, but clearly enough people are experiencing it with new or refurbished phones to indicate it affects both.
In any event, while it is interesting to measure a particular temperature at which this happens, it unfortunately doesn't really give any better idea how to
fix the issue, short of not using your phone when it approaches that temp. I suppose some people can possibly do that (my teenage kids for example), but the majority of users can't tolerate a phone that cannot be relied on when needed. Speaking personally, I had to dump mine after one too many inopportune reboot loops while trying to do business.
I still far prefer the UI of my old Dinc, but I have to admit my new iPhone does everything I need it to do, when I need it, and the battery power absolutely blows away the Dinc. The other day I was suing my GPS for a couple hours, along with lots of internet, calls, etc. and I still had about 70% battery charge by the end of the day. My Dinc would have (and preciously had) died by mid afternoon on a similar day.
I'm still pissed at HTC for not admitting or fixing this problem, but I had to just accept that the only repeatable solution is to dump the phone. Sucks, but there it is.
I almost think we are talking about two separate problems here.
Some people are saying their replacement increds are restarting right out of the box. In my experience, it takes a good bit of use for it to restart. I've narrowed it down to heat.
My phone will restart when the battery's temp is somewhere between 38 and 40 degrees Celsius. I've installed the free version of Battery Monitor Widget which can keep a running log of temperatures every 30 seconds (the time is adjustable).
I can see the battery temp graph rise over time until it goes over 38 degrees. The phone will continue to restart (loop) until the temp drops below that. 38 degrees C is about 100 degrees F, which is not hot at all.
I've replaced the stock battery with the Seidio extended batt, and that didn't solve the problem.
EDIT: Idling temperature is around 25-30 degrees C. +/- 5C.