Sounds like either an overheating condition, or insufficient power supply.

If anything is overclocked, try notching it back so the system <hopefully> consumes less power.

Make sure all your fans are working. One common culprit is the graphics card--the stock BIOS settings often don't adjust the fan speed aggressively enough. You can go into the CCC and enable clock adjustment to get at a fan speed option. Often times the fans are kept on the low side in the BIOS to reduce noise and power consumption. I've found I can usually move them up to 40-44% speeds before they start to get noisy, and this (usually) does the trick to keep them cool for the most part. A few models I've had to push to 46% or higher to keep them in check.

I would be a little concerned about that power supply... especially if it doesn't have anything to show it is 80+ or SLI/XFire certified. You may be dealing with a more generic design that suffers from output when it warms up (or as it gets older). A generic config for your system could call for about 400W for good measure (assuming stock clocks). A certified 600W model should be guaranteed to throw out 480W or more under extreme conditions, where a generic may only put out 360W (or less). So, you may not have enough head room once things heat up in the case and the PSU itself gets hot on the inside. A 650W or higher PSU may be in order.