New CPU leading to cut outs?

Hi all

I recently upgraded the CPU in my laptop to an i5. The laptop runs superbly! Or, at least it does for 30 minutes... After 30 minutes has elapsed the laptop abruptly cuts out.

I can turn the laptop on again and it runs great for exactly 30 minutes but then cuts out again.

Does anyone know what the problem could be? I know that it's not overheating and the CPU is compatible with my motherboard. I've ran stress tests on the CPU and RAM - it all passes. Also, it's not a power issue. The battery and Power Supply are absolutely fine. I've tried running the laptop on just the battery, it cut out. I tried without the battery and plugged in the power supply, it cut out.

Any help and advice would be greatly appreciated!

Thanks