Hot CPU or Bad Power supply?

Computer has Intel Core i7 860 (Lynnfield) chip.

Computer unexpectedly shuts down (like a power outage) when kids play minecraft (or sometimes during other intensive programs like youtube). I opened box and blew dust off fan and heat sink. Took heatsink off to clean underneath. Cleaned off thermal paste and re-applied before putting heat sink back on.

Core temp app says core runs about 35-40C normally at hits about 50-60 during minecraft. Still shutdown at least once. Fan didn't kick on during this though… Hmm. Other websites say 60-70C should be OK for my chip, though.

Any ideas or comments?

Use heat shink paste on processor and replace the cpu fan with newer one. Read this http://swarajbca.blogspot.in/2014/05/small-upgrades-that-make-big-difference.html

1) CPU/heatsink fan should be running all the time. If not, time to replace the fan
2) GPU (video card) may be overheating itself, check its fans if it has any
3) Your power supply may be failing, especially if heavily loaded. This is common when people add an extra add-on video card that needs too much more power, and that uses more power when gaming, causing the PSU to get overloaded

If your cpu heat sink of and use cooler past.
problem come from power supply.
if power supply ok
problem come from mother board