Need help with CPU

Hello, Merry christmas.

I have an AMD Athlon 64 X2 dual core 6400+, 8 gigs of ram, and an ATI Radeon HD 5770, with a corsair 750w power supply. My computer keeps freezing any time I attempt to play any sort of video game on it, although I can surf the web for hours and leave the computer on indefinitely and everything remains normal, just when I play games it freezes within 10 minutes. I've been told it's most likely my CPU overheating and I've done everything I can to fix that yet it still freezes. I am thinking of getting a new CPU but would like to make sure that's the actual problem in the first place before I do. Can someone please help me figure out if that's the actual problem? How would I know for sure? Also, what would be a suitable replacement for the CPU, one that will provide a nice amount of computing power but that won't overheat and give me the problems I am having now. Any help would be greatly appreciated and thanks in advance. Once again merry christmas happy holidays.
 
Are you still using stock cooling? If so you may want to consider replaceing the CPU cooler before getting a new CPU.

Here are some suggestions:
I don't know whether there is room in your case for this but if there is it is one of the best CPU coolers out there for the money right now:
CORSAIR CAFA70 120mm A70 Dual-Fan CPU Cooler = $39 ($24)

If your case is tight you might want to consider a water cooler like this one:
CORSAIR CWCH60 Hydro Series H60 High Performance Liquid CPU Cooler = $75

You didn't say what socket your Motherboard has. The AMD Athlon 64 X2 dual core 6400+ is an AM2 CPU but many boards support AM2 and AM3. If your board is AM2 only your upgrade options are limited and anything that would run significantly cooler would be much less powerful, if your board supports AM3 there are allot of options out there in AMDs current line that would be much more powerful and more efficient.
 
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