The description you gave of your problem does sound like a BSOD issue, and that you have your system set to automatically restart on system failure, which is the default system setup.
The first thing you should do is follow Jim Roseberry's instructions in post #4. This is less time consuming than other troubleshooting steps, such as checking for bad RAM, but could quickly reveal the problem.
Once you disable the "automatically restart" on system failure, you can narrow the cause down. If you get a BSOD after disabling "automatically restart," see if it tells you, at the bottom or top of the BSOD screen, what is causing it. And if the BSOD lists what's causing the problem, you can go from there.
Once you disable the "automatically restart" option, if your system reboots again and you get no warning, you can start looking at other possible causes such as a bad PSU or bad RAM.
Also, it helps if you list your system specs.
Goodluck with resolving the issue.