Adding a case would not help with the heat issue in any case. If it's a plastic/rubberized material,you would not feel the heat easily and when you would, it would be much more without the case.
Leather/fabric cases on the other hand would allow for easier heat dissipation through you feeling the heat much quicker in your hand, but then again, that does not help with cooling.
I came across some solutions, but they employ fans for cooling and having a fan 10 inches from your face would be a less than ideal experience while on an iPhone.
Look at the possibility of limiting background apps. That whould be a better solution, but the phone will get hot again. Best you can hope for is using a case that does not allow heat through too quickly, and can maintain it's life in the process. For this purpose, leather cases have been good enough in my experience.