Help me?

Try checking your CPU cooler's contact with your CPU. You may have to reapply the thermal paste and seat it correctly in there . Since your heat sink isn't getting hot and your computer is shutting down it might have something to do with it overheating due to poor contact with the cooler.

First we need to know your PCs specs.

Get 3 softwares (all of them are free):

Speedfan: this will tell you your CPUs temp

Prime 95: this is a torture test for the CPU, once installed it will ask you which test to run(select the test that stresses the CPU).

MSI afterburner: This reports your GPUs temp and frame rate when you play games.

Step 1: install speed fan, run prime 95, tell us the max temp your system hits after 15mins (if it can last that long that is). If your system makes it past prime 95 then its time to test the GPU.

Step 2: install MSIafterburner go to the settings menu, click the monitoring tab, Tick the options which mention GPU temp monitoring and click ON screen display. When you play games now u will be able to see your GPUs temp.

Tell us both these things and we may be able to help.

Edit: as the above poster mentioned if your heatsink isnt getting warm then its highly likely that its not seated properly. In which case i would recommend you youtube some videos on how to apply thermal paste and how to seat the heatsink (after which u would have to run the prime 95 test to confirm things are stable).

I had someone test my CPU and temperature.

ok so what was the verdict? seems you dont want much help if you are being vague about the situation. What did this person that checked out your CPU and temp say? Did it rule out what we are saying is the problem? If so we need to know so we can move on to different possible issues you could be having.