Stock Battery and phone temperature

[npark2012]

So it's been annoying me how the battery doesn't last very long and I was considering getting an extended battery until I saw the size of the thing. I just can't use the extended battery that's as big as the phone, plus I need some kind of protective case for my phone and most will not fit. So I am considering just getting a battery pack that I found on Amazon 10,000mAh should do the trick but now I'm in the situation where I would charge my phone twice a day (with a little over moderate use) and the phone does get very warm when screen is on for more than 20 minutes.. around 110-118 F
So does anyone have any tips of cooling down the phone while still being able to be on the phone longer or should I just bite the bullet and get an extended battery like the seido or anything? And let's say I do get the extended battery, my two questions are, will my phone still get very warm? and what cases are out there that would fit like sa 3800 mAh battery that has equal to or better than the protection provided by my current otterbox commuter case?