There are multiple software and hardware reasons that might cause an unexpected shutdown.
Other than the shutdown, what leads you to the overheating theory? Was the fan going full tilt before it shutdown? Was it warm or hot to the touch underneath? Did you have it on a soft surface that would block the vents that are underneath it at the back?
If a Mac will not boot when you press the start key, hold the start key down for ten seconds and then try booting it. I know I'm scared when my Mac won't boot but when this has happens to me (infrequently) a little patience and playing with the power key fixes the problem.
If it was not heat related a more likely scenario is a kernel panic. See http://support.apple.com/kb/TS3742 .
If it happens again in the next few weeks and the kernel panic page does not help, or you want a diagnostic test for any reason, make an appointment to see a Genius at an Apple store. Genius reservation http://www.apple.com/retail/geniusbar/ . A diagnosis and repair will be free on your 1-year warranty. While there consider signing up for AppleCare to extend the warranty and free consulting to 3-years.
P.S. Be sure you have it backed up. https://discussions.apple.com/docs/DOC-4055