I used to have overheating problems on my HP Pavillion G6 (AMD Trinity Model) and it used to hibernate after 10mins of gameplay. So after some basic surgery and blowing lots of dust it is working fine. Now you could go to a service center for this but that's not how we do things at TE, right? 
Learn how to fix overheating problems in your laptop by cleaning its fan and reapplying thermal paste. This video also shows the dis-assembly process for the HP Pavillion G6 laptop (last year's model) with common steps that you can apply on any recent consumer laptop:

Learn how to fix overheating problems in your laptop by cleaning its fan and reapplying thermal paste. This video also shows the dis-assembly process for the HP Pavillion G6 laptop (last year's model) with common steps that you can apply on any recent consumer laptop: