Mac Mini keeps shutting down while exporting from iMovie

For some reason, every time I go to export my video in iMovie, about 15-20 minutes (give or take) into the process, I get the grayed out screen with "Restart your computer now". It's happened twice so far. Any ideas on what could be causing it? I am using a Mac Mini running OS X 10.6.7, the video is about an hour and 45 minutes long, and I am exporting to 720p.

Any assistance would be appreciated!

Exporting a video puts the processor under high load, making it generate a lot of heat. Might be a good idea to check the heatsink for dust and renew the thermal goop.

MUCH more likely that you're running out of temp hard drive space. For an HD video of that enormous length, I would make certain you have GOBS and GOBS of free hard drive space left. Several dozen GB at least, I should think.