I think it's simply the fact that your system is falling apart, and has NOTHING to do with GT6. As someone mentioned, it may be dust, so you may want to open it up and clean off ALL of your components. Or, your CPU and/or GPU could be falling apart... In which case, you may want to look into a new mother board, and a tutorial on how to swap them out. You'll need to be certain to find the correct product model if you do - which is probably listed somewhere in your settings.
My PS3 (fat, 80GB, Backwards-Compatible) died after a little more than half an hour of playing Burnout Dominator (PS2 game), and the console wasn't even hot. I fixe this, and a few months later after a good 6-hour GT5 session, I turned on my PS3 only to get another YLOD next day. My CPU or GPU disconnected, and just needed to be reset (look up how to fix a YLOD on YouTube - there's a 3-part tutorial that got mine going).
I don't know if the board-resetting thing will fix yours, since it doesn't sound like a full-blown YLOD problem, so it may simply be that part of your board is starting to fail. It's less expensive to get a new board than a new console, for sure. And I don't think you'd have any warranty left on your PS3, considering how old it is, so I don't think you can do wrong in cracking it open, unless you don't know what you're doing. But the tutorial I mentioned should allow you to get it done either way.