No, nothing is running causing the CPU to run hot. It cools off quickly if I go into a temp controlled room. The screen is not staying on.
Ok, that narrows it down a little.
Have you looked inside developers options to see what is running continuously?
Using an app like Greenify to force stop unused apos when the screen goes off is a great way to save some power, and can help the device generate less heat.
This may not be much, but if you have an app that runs all the time that sucks down 200MB of memory, it can be more than you think.
I had a great launcher that I loved- Apex Launcher.
The launcher was great- used about 30MB or so, which is about normal for a launcher.
What wasn't normal (or perhaps it is normal, and so I look out for it now) was the +200MB that Google Analytics was using with that app.
And yes, I noticed a definite improvement in temperature, battery life, and device performance when I dumped that app.
Another thing to discern is whether or not you still have this overheating issue WITHOUT a case.
I have never used a case, and have still had the issue at times.
Leave the phone in the car?
Bingo.
Leave the phone in the tent?
Yup.
Leave the phone in the shade, to come back and find that the sun has moved enough that the shade is no longer on the phone?
Ditto.
You may need to take the measures to just not have your device in such an environment.
Especially if the battery is not easilly removeable.
That is the part that suffers the most from heat.
Yeah, yeah, I know.
But we don't have them on us in the shower, either.
There are some places that we just cannot take our devices, because the environment is unsuitable for them.