Well, based on some of the responses to this thread and some other posts elsewhere in this forum, I've tried a few things.
First, I removed my NIC, secondary video card, capture card and sound card, and took out half my RAM. Now 3Dmark2000 runs for nearly a minute before freezing. If I spray canned (cold) air on the CPU, it runs for 2 to 3 minutes. Since I've been running with the case open, and I'm using a PC Power & Cooling power supply (300W) I think my problem lies elsewhere.
Second, I left the machine running all night and all day playing a MIDI file (very low CPU utilization). No lockups.
I'm thinking at this point that under heavy load, perhape the K6-2 500 is drawing more current than the voltage regulator can supply. I'm going to try installing a K6-2+ next, which draws about 33% less power. It will take me a few weeks to do this, but I'll let you know how it turns out.
-ken