It could be a static prob or heat but its more likely to be your OS (Operating System) or your HDD or your network.
The way to roughly check if its Memory / processor is when it lockups does the mouse still work and or does the scroll lock / num lock light still toggle?
if they do then it proves that the CPU , motherboard , vid etc are still running.
To test if its the Network disable the network card (Right click on the card icon and select disable) and reboot, then work locally for a while (Sorry no landyzone) playing a game or something.
If it locks up then we need to start looking at what was running at the time and what you have installed.
Also check your event viewer and task manager.
If you find a unusual event in the event viewer try looking it up on
EventID.Net
Good luck as this is only a start in looking for a prob.
Ps
A good rebuild once in a while clears a lot of problems