Why is my iPhone 5S overheating so much?
Although there are several other answers, I'll contribute my own $0.02 for future readers as well.

The device is overheating due to processes consuming the device's physical memory and is causing it to overheat. Activities like calling and data usage often requires a lot of battery power, which then leads to the device over-heating.

Some temporary solutions would be to:


If you are standing in the sun, remove the device from the heat.
Closing background applications when not using them to avoid battery consumption.

This also includes disabling WiFi and/or service when not in use.
Games are very bad at power consumption, "Clash of Clans"  being a major example using up to 10.3mAh/min sometimes even when not in use.
Avoid the use of 3rd party cables (as mentioned by another user who answered).

Put your phone into sleep mode every once in a while the system can cool down and regain some of the used RAM.
Delete some apps, the less apps using your battery and memory the better.




As for long term solution, get the new phone. Even though the device heating to rather hot temperatures can be normal, after a short period of data usage it shouldn't. Often times it is some faulty hardware that is causing the problems.

If you aren't in the situation to get a new phone, then a factory reset is the way to go. This will delete any apps or cached data that would be causing the battery over-consumption and would restore the device to its intended factory abilities.

Hope this helped!