Underclocking

I've been really pulled in by ultra-thin gaming notebooks like Gigabyte's P35G (V2-CF2) and MSI's GS60, both of which come with either a GTX 860M or 870M. However, I've also heard that both run quite hot - as in irresponsibly hot. Would it be possible/easy to underclock and undervolt the GPU...

I wanted to buy a computer on a 500$ budget, and I realized that I had a performance cap. Anything that performs better than that is indifferent to me. The cap would be playing league of legends at lowest settings with little or no heat. If I can find a laptop that can do this, then it would be...