Update since my reply a month ago.
Shortly after posting, I took the unit apart and looked for problems. There was a little dust, but not much. Heatsink seemed a little loose on the CPU, but could be normal. I usually crank mine down pretty good so I'm not used to any play.
Cleaned out the little dust that was inside. Cleaned off CPU/heatsink interface and applied AS5. Reinstalled heatsink and cranked it down firm.
It's run 24/7 for the past month with no problems. Then tonight I'm surfing the web and it shuts down. I restart it, and about 10 minutes later it shuts down again. Now it's been running about 30 minutes or so. This is all on AC power, stock speeds.
It seems like whatever it is gets worse with time. Each time I've made a corrective action (first time was reverting from overclocked to stock speed, second time was applying AS5), it seems to fix the problem for a length of time, but it eventually returns. At this point it seems like the only option left is to deal with it until it gets unbearable, then eBay it for parts and get a new laptop.
Makes me regret purchasing eMachines. Seemed like a great deal at the time. First problem was the cracked hinges. Got replaced under warranty, now the right hinge has cracked again. And this thing is BABIED. Rarely ever leaves the AirDesk, and even then it's to occassionally roam upstairs. Now this problem, and it's no longer under warranty.
As a rule, I never buy any type of ESP on anything, and have 'saved' thousands of dollars over the years and consistently turning it down. Maybe I'll start making an exception for laptops. First one I owned did OK, lasted about 3 years. Second one lasted about a year and a half, then had a problem with the video card. Parted it out and bought the M6805 about a year and a half ago, and it's already unreliable.
This is one of the reasons why I haven't bought a packaged desktop in about a decade... you can't get to any of the BIOS options unless you build your own. This could probably be solved by raising the setpoint or just turning off the auto shutdown on high temp option. Could potentially lead to a fried CPU, but then again, at least I wouldn't have to worry about this problem anymore.