Just an update (also posing same questions to "support):
OK, during a particularly "bad" evening with this problem, I believe we can discount anything to do with the Windows operating system.
Once, before the "Windows" logo screen was displayed, I got the high-speed fan followed by the shutdown. I waited a few seconds, powered the machine back on, and boot into BIOS. This time, while just sitting on the first BIOS screen, go the high-speed fan followed by immediate power off. This time on battery, a couple of days ago, this occurred while plugged into the brick.
The only particular difference this evening? Well, we're in Georgia, and tropical storm Arlene is sending us occasional bands of rain, needless to say the humidity is a little higher than usual, but nothing else of particular note.