Thank you everyone, who has participated so far.
Here's a test sequence that I just completed, with a stopwatch.
Start up cold... in an air-conditioned room... with the back uncovered and propped up to allow airflow underneath.
* Starting baseline temp = 49C
* Ran SetCPU stress test for 3 minutes. 80C
**Waited 1 minute to cool a little.
**Ran SetCPU stress test for 5 minutes. 84C
**Waited 30 seconds to cool a little.
**Ran SetCPU stress test for 4 minutes. 90C
**Waited 30 seconds to cool a little.
**Ran SetCPU stress test for 3 minutes. 88C
**Waited 30 seconds to cool a little.
**Ran SetCPU stress test for 3 minutes. Boom, reboot at almost exactly the 3 minute mark.
So that's 18 total minutes of Stress Testing with 4 brief random breaks in between. And finally a crash.
When I picked up the A700 after each stress test stop, the back was hot. I'd call it uncomfortably hot but not "burn my hand" hot.
Resetting my display timeout to 30 minutes, then am going to run one straight stress test. Let's see how long it takes to force a reboot.