Rob Salamone, I would start by replacing the battery as well as the screen. It is possible that you have a damaged battery charging circuit and that is what heats up your phone. Check around the MAX8987 DC Power Management IC and see if you notice anything corroded or charred. [guide|5861|Here is] a teardown that will give you an idea how to get to the parts to be replaced. Attached image from [http://www.techrepublic.com/photos/cracking-open-the-samsung-galaxy-s-ii-sprint-epic-4g-touch/6305124?seq=35|here]
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