yes that does sound like a heat problem.

I suppose you're using the stock heatsink?

the clips on those are quite silly, that's where I'd look first. Are all 4 corners down into the mobo properly?

Check your power supply dude... my have some problem..

Check your processor if it is correctly installed and fitted in the cpu slot of your motherboard. Incorrect pib installation would lead to overheating and abnormal shutting off of the unit. Your RAm, video card and psu should also be checked.

Make sure you've got the right amount of heat sink paste on your cpu and heat sink. Best to use a good quality one, maybe silver paste. Smear a thin layer of the stuff so that there is good contact to the cpu. Also make sure you blow out any dust from any fins. Also make sure the fan plug is connected the right way round, unlikely but you never know!
Also check that your memory is seated properly. Take them out first and clean out the slots.
The problem could also be caused due to faulty periferals. Maybe your mouse is faulty, or your web cam.
Possibly a software problem of which case you might need to reload your Operating System and programs. Make sure you back up what data first.
As with the ram, make sure your graphics card is seated properly and make sure the slots are clean.
Unplug any periferals that are not in use, like your scanner or any other usb products lying dorment.
The idea is to troubleshoot!