I'll bite...
I know so little of other important considerations that may pivotal in this diagnosis - but I'll go to general causes first. It's only a year old and I'm unaware/unsure of the exposures/abuses that it may/may not have faced. If you have dealt with taking a laptop apart, then you may want to remove a lower panel that may give you a better view of the motherboard. If you haven't; then it may well be time to take it to a qualified repairman
Don't assume that the CPU is being adequately cooled; the condition you described is typical of a CPU overheating. If you can see the CPU heat sink and it is free of debris (cat hair is a killer, but any collection of lint and dust will also insulate the heat sink='trouble'). If the thermal paste has ozzed out, then the lack of cooling provided by the thermal paste between the CPU and the heat sink may also be the cause. Don't do this if you don't know what you are doing, you could make it worse than it is. If it ust be replaced, I suggest Arctic Silver - which is one of the finer thermal pastes available on the market - and supersedes any other by far. You started this question with some doubt that heat may be the cause. So I entertained that premise first.
There may be other components on the motherboard that is failing/intermittent when the laptop has reached operating temperature. Let's hope that isn't the issue, or it could get costly.
I'm not going to overlook the other obvious factor. The operating system may be a cause. Check your system files to be sure that all of the drivers are there; if the system files shows errors that could cause the OS to reboot. Not common, but it has happened before. Chances are you have Vista, and there have been many issues like this and others that cause issues with hardware that may be tied to shutdown.
The power supply/battery charger may also be an obvious failure. I run my battery condition icon in the tray to monitor the battery's charge/state. You can check that out when you start it up; it's usually in lower tray on the right-hand side.
If your laptop fails these most obvious and detectable causes above; then I suggest to contact the vendor who sold it to you and see if there is any warranty repairs or recalls that may have been issued for your unit.