Guess what? It died again.
This time I took a look at BIOS stuff. Fan rpms (approximately, two of them changed): Processor region: 3000 Rear: 1500 Front: 0 Perhaps that is my problem. I do have more fans lying around somewhere.
The last even the BIOS logged was from 2008. In case it matters, the BIOS version is BF86510A.86A.0038P08 .
On boot I got a message saying that the CPU was being throttled because it was over the temperature threshold. IIRC the BIOS said that the CPU area temperature was about 80 C.