What Power Supply are you using?
What temperatures is the CPU running at when the computer turns off?
What applications are causing 100% CPU usage?
Press Ctrl+Alt+Del to bring up the task manager. Can you shot us a screenshot of what applications are using up so many CPU cycles?
Have you checked your system for a Virus or Malware? Try this free online scanner to make sure your system is clean.
The situation that you describe doesn't sound like a defective CPU to me. It sounds to me more like the CPU heatsink fan may not be running at the proper speed or the HSF has a lot of dust that needs to be cleaned out. By design the CPU will shut itself off if it reaches a certain temp, often 80C on FX processors. This is to prevent damage to the CPU. I'd check to see if the HSF is running and if it speeds up when you are running multiple applications or games, etc. Some mobo BIOS have adjustments for fan control. You might need to set the fan speed to 100% for proper cooling under heavy loads.