A German engineer has claimed to discover why the MacBook randomly shuts down. Here’s the translated explanation and solution according to Martin Backschat’s blog and CrunchGear:

The heat sink expands during operation and gets into contact with the sensor cable and melts the cable’s isolation. This in turn causes a short circuit and, thus, the immediate shutdown of the Macbook. As the heat sink is cooling down, the heat sink contracts to the point that it looses its contact with the cable and breaks up the short circuit.

and the solution:

A solution is to bust open your case and place some insulation tape around the affected areas of the sensor cable. Once you do that—unless the tape melts also—there should be no problems with sudden shutdowns. Though this procedure may or may not void your warranty. You may want to just wait until Apple acknowledges and fixes this for you.

We have yet to see any confirmation that the fix works, or if that is truly the cause of the random shutdowns. Opening your MacBook in such a manner violates warranty and has the potential for doing more harm than good. We would continue to recommend contacting AppleCare directly rather than attempting a fix it on your own.

Discuss this in the forums.