But wait! Here's Paul Harvey with The Rest of the Story!
After running Windows and doing a fair amount of processing, Windows rebooted to install about 1800 updates it wanted since the computer went down. But when it rebooted, it wouldn't start up again, giving the thermal event message and shutting down immediately.
So I thought about the other half of the issue mentioned above, the plug connectors on the back of the case. But I remembered this case has the power supply in the lower front of the case, and the plug on the back of the case is just a short power cord shunt to the bottom of the case where the power supply is.
So I turned the computer on its side and plugged my best A/C cord directly into the power supply on the bottom. No joy. So I decided it must be a power supply issue. I had noticed the internal PS lights varying in brightness, so I had a feeling about it before anyway. Luckily I had a very high quality PS in reserve, so I put it in, and the computer has been happy both last night and this morning!