Cooling fan speeds then cpu shuts down - Dell OptiPlex GX620 PC Desktop

1. Stop Overclocking your CPU
2. Make sure your Heat Sink is placed properly above the processor
3. Clean the Processor fan, Heat Sink and other peripherals
4. Use High Speed fans
5. Use CPU Heat Sink Paste in the processor
6. Make sure your dint restrict the speed of CPU fan.
7. Use Additional Cooling Units
8. Check your SMPS
9. Use proper ventilation in your room
10. Shut down your computer at least two hour a day
Let me know if it helps you.
Use system utility tool like RegInOut to remove unwanted files , fix registry and windows errors which cause of heat problems

When the CPU overheats then it will shut down (i.e. thermaloverload) and won't boot up again until it has cooled down. If this is theproblem is not fixed then the CPU will eventually fail.
A faulty fan causes the problem or the fan and heat sink assembly are cloggedwith dust.
Check the CPU fan to see if it spins freely, if not replace the fan.
If the fan and heat sink is clogged with dust the remove the dust and make surethe vents are clear and dust free. Use a small brush and can of compressed airto do this.

Following are the reasons for overheating, just take care of these things::

• Stop Overclocking your CPU
  
• Make sure your Heat Sink is placed properly above the processor
  
• Clean the Processor fan, Heat Sink and other peripherals
  
• Use High Speed fans
  
• Use CPU Heat Sink Paste in the processor
  
• Make sure your dint restrict the speed of CPU fan.
  
• Use Additional Cooling Units
  

Also use a system utility tool like PCFresher to fix windows errors.

Since your PC is two years old its recommended to check your computers hardware check your cooling fan
specially CPU cooling fan if that fan is broken your pc wont work and be careful turning on your PC again and again will burn the processor

Try blowing out any dust from around the fan with compressed air. If the fan is turning on and off a lot, this could be normal, depending on your processor, but if the system just shuts down fully and randomly, it would be a heat issue. The CPU is overheating and the failsafe mechanism is to instantly shut your computer down. The only way to avoid this is to raise the CPU shutdown temp in the BIOS settings, or if you can access the CPU, remove it and apply new, quality thermal grease. Also, ensure the fan is operating correctly during use and dont block any air intake or exhaust ports.

A overheating CPU will shutdown and won't start up again until the CPU has cooled down.
The overheating problem (ie. thermal shutdown) is most likely caused by a faulty CPU fan or dust clogging the CPU fan and heatsink.
Check the BIOS CPU fan speed could be set too low, check the fan speed/temperature setting.
If this problem is not fixed, then the CPU will eventually fail.
Check the fan to see if it spins freely, if not then replace the faulty fan.
If the fan and heatsink are cligged with dust, loosen and remove the dust and use a can of compress air to blow away the dust.

That sounds like the cooling fan is either plugged up, or it is faulty, or the cooling fins for the CPU heat sink are plugged up with lint and dust. The cooling fan on that toshiba should be accessible through a cover panel under the pc notebook. Remove the cooling fan and use compressed air in a can to clean the cooling fan and the cooling fins to the CPU heat sink and be sure that the air intake vents for the cooling fan are also clean and free of any dust, dirt, or lint. Here are some images that are similar to help assist you, and let me know if you require any further assistance.

A laptop locks up or shuts down when it get very hot. The CPU shuts down (thermal overload) when it overheats and will not boot up until it has cooled down. If this problem is not fixed, eventually the CPU will fail.
This problem could be caused be a faulty CPU fan and/or the CPU and heat sink assemble is clogged with dust.
Check the CPU fan to see if the fan blade spins freely (it may have a seized bearing), if not replace the fan. If the fan and heatsink is clogged with dust, clean and remove the dust.
If additional cooling is required and there are ventilation grills on the bottom of the laptop, then purchase a laptop cooling pad. Place the laptop on the cooling pad, these pads have fans that direct air into the grills at the bottom of the laptop.

If the CPU fan speed is too slow or not working at all, the computer will shut itself off automatically to prevent damage to CPU from overheating. You may end up having to throw more money at the problem and get a new fan. I went to Compaq's web site, looked up your particualr computer, found out what type of fan you needed, and I did some research. I recommend getting the fan in the following link. It's very cheap, and has good reviews. The other fans on the site all have bad reviews. Hope this helps.

http://www.newegg.com/Product/Product.aspx?Item=N82E16835114011

check with the temperature of the CPU core!
because of over heating the CPU is shutting down or not.