Just Video or does it crash while
doing other things too.
Most of the video on YouTube is Flash Video which is a resource hog on Macs, not just iMacs, and can cause overheating really quickly.
Try joining the HTML5 trial that is going on at YouTube and see if the same crashes happen.
you can join the HTML5 trial by signing into your YouTube account, or get one and sign in, and on the next page check out the "What's new" section
Click on the HTML5 link and from there you can opt in or out of the trial/beta
While you are at it, you might want to check that you have the latest version of Flash installed.