You need to provide your motherboard, case, and card layout. This sounds like an airflow problem, but it'd be better to not guess.
The problem you have described could be caused by an overheating graphics card. What is the current temperature of the graphics card after playing games? You can monitor the temperature via the Catalyst Control Center or AMD Radeon setttings.
How is your case airflow? Does the graphics card have plenty of room to breathe?
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