iPhone heat and battery drain
This happened to my 5S as well. It had a light spot on the screen and it was separating from the casing as well. 

I'd suggest bringing it to the apple store to have them check it out. They should run diagnostics on it and determine if it is a battery issue. When I brought mine in, the diagnostics came back ok, but they still offered to replace my phone in its entirety for $79 (the price of the battery). 

Since then, my new phone has worked perfectly, so hopefully that is the case for you.