PC overheating and shutting down?

So I have an old pc that I ecided to fix up so I orders a new power supply and more RAM and all of the sudden the pc keeps shutting down even when its not very hot. I think its the power supply(i bought it on Amazon and it had good reviews, no one talked about this) the computer is dusted out and the only things I think it could be is the thermal paste or power supply.

SPECS
4 GB ddr2 RAM
3.17 GH AMD proccesor
New PS:http://www.amazon.com/gp/product/B008MUD9IK?psc=1&redirect=true&ref_=oh_aui_detailpage_o04_s00
if any other info is needed for you to help me tell me please.
Added (1). I have been working on the PC for a while and it was doing this but rarely
Added (2). Update 2.40 Ghz

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