iPhone 5s battery gets super hot then shuts phone down. Is there a solution for this?

The heat is probably caused by the iphones batter being overworked. Something is causing it to drain, and that's leading to the heat you feel. So the best thing to do is try to figure out why the battery is being overworked. Heres are few things I googled that might help:

http://tinyscreenfuls.com/2012/11/iphone-gets-hot-battery-drains-rapidly-how-i-f ixed-it/

https://www.maketecheasier.com/why-is-iphone-overheating/

If it shuts off there's a hardware problem with the phone. No software on a non-jailbroken phone can cause the phone to overheat like that unless the phone is in an environment over 90º F. Make a genius bar appointment.

Not true. There is no software that can cause a non-jailbroken iPhone to overheat. If it overheats it is being used in an environment that exceeds the operating temperature range of the phone, or it has a hardware problem. Which may be the battery, but it could be a dozen other hardware problems.

The phone might be overheated because of an software issue or the battery need's replacment if that is the case .
It might also be on the motherboard, it is overhetaing the battery for some reason.

Charlie,

Are you playing lots of energy intensive games for long periods?