HP ENVY 14 i7-940: GPU overheating when charging?

Hi,
I'm having troubles with my HP ENVY 14 overheating (specifically, the GPU is overheating.) The specs of my machine are:

• ATI Mobility Radeon HD 5650 (obviously)
• i7-940
• 8GB RAM
• 256GB SSD
• (not the Beats edition)

When playing video games (even Half-Life 2, a 7 year old game!) sometimes the computer would randomly shut down. This ONLY happens when charging. Upon investigation, I found this event in the Windows Event Log:

I then ran stress testing on the CPU (Prime95) and there was no overheating. When I ran stress testing on the GPU (Furmark) the computer shut down after a few minutes of testing with the same log entry. This leads me to believe that the GPU is the part of the computer that's overheating.

I have tried:

• Making sure all vents are unobstructed (they are)
• The laptop is on a flat surface (my desk)
• Calling HP (they were helpful, but told me my best bet was buying a cooling mat for the computer, something I would like to avoid if possible)

I think my brand-new computer should be able to play at least Half-Life 2 for more then a few minutes! It never overheats when not charging but obviously games are not playable when this is the case because game performance vastly decreases when not charging.

Thanks for any help you can provide.