System shuts down in 1 and 1/2 hour.

Hello,
I have a i5 2400 cpu, crosair 4g. System shuts down at 1 or 2 hours of usage. It gives out 3 beeps and then shuts down when i try to reboot it again. It starts successfully for another an hour or 2 if powered on after 6-12 hours gap. The whole story repeats again.

What I've tried:
Assuming that it was a thermal compound issue i've tried changing the thermal paste.

Now i'm guessing it is a memory module problem since the motherbord gives 3 beeps.

I'm going to do memtest on the ram.

Can it be any other issue? Am I on the right path? Can you guys help me?

Thanks a ton for stopping by to read my query.