Computer Just Shuts Down

i am currently working on a computer that when it is on for more than like 15 or 20 min it just shuts off no warning. it is a windows xp compaq 4400US itz kinda old but it needs to be fixed. i figured that it was a heat problem like the cpu was over heating.l so i put a couple of fans in there one in the back which blows warm air out and on in the front whick blows cool air in. i put a Antec Cyclone Blower Fan in a pci slot, a Antec Blue LED 80mm Fan in the rear blowing warm air out and a Antec 80mm TriCool DBB Fan in the front blowing cool air in. they all Cool at 34 CFM or so so if anybody could just give me some ideas that would be great thanks scott