I have 3 year old computer that shuts down automatically after 15 minutes. Since all the fans are working, I don't suspect a heat problem
So what else could cause my computer to shutdown like this?
You cannot just assume that it is NOT a heat issue. Just because you hear a fan whirl. Heat buildup could be caused by dust clogging a fan, or building up around cooling fins (video cards, etc).
Please update what operating system you are running. In many cases, having a look @ (windows) event logs will give you an idea WHY something shut down. IT will log those things for you to review, sometimes it could be a failing video driver and it notes something like ati.dll failed to blah blah which hints at it being an ati video card issue (yes ati/amd).
Update your question and post more details, otherwise people will just guess.