If you say that the fan is fine, then it’s got to be something else. Had you made any hardware or software changes since it started to turn off on you??

Sorry for the delay, I've been out of town. OK, I added the 750 GBHD that HAD peen a Westeren Digitial My Book external Hard Drive. That gave me a total of 4 HD. I then reformat all of the drives (Backing each one up to the other as I reformated, so that I had one blank one left) Than installed a fresh copy of the OS an on 30 GB partition of a 250 GB HD I had.

Hi. HDD don't really have much to do with this then. If fans work fine, they blow air, and the CPU is still getting hot, then let’s turn to Google, and see what other have to say to this.

This is From Google:

Heat related issue
A computer that turns off without warning is often a heat related issue. Many computers today are designed to turn off or automatically reboot if the computer, processor, or other device in your computer gets too hot. If you have heard any abnormal noises coming from your computer recently such as a high squealing, this could indicate a fan may be failing in your computer.
You can first start by verifying the fan on the power supply is working by examining the back of the computer and seeing if the fan is moving and moving smoothly. For all other fans in the computer, you will need to either open the computer and make sure the fan are working (processor fan and case fans) and/or if your BIOS monitors the RPM of the fans, enter BIOS and make sure the BIOS does not report any errors.
While inside the computer it's also a good idea to verify the processor heatsink is properly connected by disconnecting and reconnecting the heatsink. If the processor heatsink is not properly it will not keep the processor cool causing the computer to overheat.
Users may also be able to determine how hot their computer is by onboard thermal sensors. If your computer comes equipped with these sensors, make sure your CPU is not running to hot; additional information about how hot your CPU should be running can be found on document CH000687.
Hardware issue or error
Any failing hardware component in your computer could cause your computer to unexpectedly turn off without warning. If you have recently attempted to add a new hardware device, remove that device to make sure it is not causing your issues.
Before attempting to remove any hardware, make sure you are not encountering this issue because of hardware conflicts by viewing Device Manager for errors. Additional information about Device Manager can be found on our Device Manager page.
If you have not recently installed any new hardware into the computer, the next best solution to determining if this is a hardware issue would be remove any hardware on the computer that is not needed. For example, remove your modem, network card, sound card, and any other expansion cards that are not needed for the computer to operate. Run the computer without these cards to see if they are the cause of your issue.
Computer virus
It's possible for your computer to be infected with a virus that is designed to shut down your computer or turn it off. If your computer seems to be turning off when executing a certain program at specific times in the day, it could be infected.
If you believe your computer may be infected with a virus or are uncertain if your computer is infected with a virus, make sure your virus scanner definitions are up to date. Additional information about checking this can be found in document CH000533.
Issue with operating system



If after following each of the above recommendations your computer still continues to reboot, it is likely that you are experiencing a Microsoft Windows operating system related issue that cannot be explained. To help make sure this is the case, please try the below steps.

1. Reboot the computer and enter CMOS setup as the computer is booting. If you are not familiar with how to enter CMOS, please read through document CH000192.
2. After you have loaded the computer in CMOS setup, let the computer sit.

If the computer does not turn off while letting the computer sit in CMOS, it is likely that you are in fact experiencing an issue with Microsoft Windows or your operating system and it is recommend that if you have followed all of the above recommendations that you reinstall your version of Microsoft Windows. Additional information about erasing the computer and starting over can be found on document CH000186.
Other failing hardware

If after reinstalling your operating system, or during the installation of your operating system, your computer turns off abnormally, it is very likely that other hardware is failing in the computer. Often this is RAM, CPU, Motherboard, and/or Power Supply (in that order). If you have extra available parts or have a friend or co-worker with a similar configuration that is willing to allow you to test their hardware in your computer, try swapping these parts to determine if they are at fault. Otherwise, you will need to have the computer serviced.

P.S. Don't mean to disappoint you, but if your motherboard fryies in a bit, don't be surprised. I had exactly the same symptoms on my OLD Dell Demi E521, TWICE!!