I’ve used Thinkpads for a long time for the relative build and BIOS quality, although recently I switched to the Panasonic Y series. I still have an IBM R32 for guests to use but recently it began blue screening randomly.
The symptoms were that it would run ok for a while, a couple hours to a few days, and then would get a STOP error in ati2advg.dll. Often, it would do this when beginning to play a video. I had tried various combinations of video drivers with little change. RAM tests showed no problems.
I found on various forums that the T42 and possibly other systems had a build problem where picking up the laptop by one corner would cause a heatsink to momentarily detach from the chipset, resulting in a similar blue screen. This sounded familiar, so I disassembled the laptop. (Disclaimer: doing so voids your warranty, I take no responsibility for your actions.)
Getting a copy of the hardware maintenance manual helps find all the screws and tabs. On most laptops, the first step is to get the keyboard removed and then other screws become accessible.
As you can see, the heatsink for the graphics chip is merely a piece of aluminum tied to the drive bay. It had a bit of sticky tape between it and the chip, but it didn’t make full contact with the chip below.
After removing the CPU and graphics chip heat sinks, you can see the CPU on the upper left and the graphics chip in the multi-chip module near the center. Since the chips on this small module are in an L-shape and the heatsink was centered, it only contacted the very edges of each of the chips.
I decided this was likely the problem, so made a new heat spreader for the graphics chip while avoiding adding much weight. I took an old punch-out panel and cut a rectangle using my Dremel tool.
After cutting, it looked like this:
I put some heatsink compound on it and attached it to the graphics chips. To keep the corner from shorting out against the solder pads, I put a small square of double-stick tape in the empty space of the “L”. This helped secure the heat spreader, although I’m mostly depending on pressure from the heat sink to keep it in place. I then reattached the heat sink over it and reassembled the laptop.
When reassembling everything, be careful! The screws that hold the CPU heatsink snap extremely easily. Once they stop moving under even gentle force, don’t push them any farther. I ended up fabricating some out of some old parts. Don’t make the same mistake.
I’ve run various stress tests, including accidentally leaving it in the sun for a few hours and it hasn’t crashed since. The keyboard above the chip also feels noticeably cooler.
rdist 
Actually, disassembling a Thinkpad doesn’t void your warranty, at least on the eastern side of the Atlantic. This is illogical, as how else could IBM/Lenovo provide user serviceable parts?
Best regards
DZ
From everything I could see on Lenovo’s website, opening the case (other than the slots for RAM) voids the warranty. They don’t sell any parts to users here, just ask you to send the whole thing in for them to swap parts. And of course, my R32 is long out of warranty so it would cost a lot to get it fixed.