The g series of laptops actually above a robust cooling system. You'll still be warm under heavy load, but usable.
Since you asked...
The problem is that the laptop is ridiculously heavy and still performs worse in games than even a low end gaming desktop ($600 range).
I say the ideal solution is to build a decent desktop and buy a midrange laptop. You'll normally come out around the same price, and you'll get a laptop that is good at laptop things and a gaming computer capable of handling most games at moderately high levels.
If you have a need for extreme power on the go, this all goes out the window, obviously. Among gaming laptops, you've chosen a fairly good one. I'm just not a fan of gaming laptops in general.