The subject line says it all, if there's no room left in the temporary directory then Paint.NET eventually dies with an uncaught exception. Reproducing it is a bit vague since it consists of two steps:
1. Set up a temporary directory with very little or no space left (e.g. on a RAM drive or a USB key).
2. Do things until Paint.NET dies with an uncaught exception.
I've tried it a couple of times and the most reliable way to get it to crash seems to be to create some new image and then try and save it, e.g. as a JPEG. When you tell it to write to disk (i.e. after setting the filename and quality factor), Paint.NET bails out with an uncaught exception.