Re: Gs4 seems to be running hot.
These phones are thin and have ridiculously powerful processors all stacked up and squeezed next to each other along with a ton of sensors, memory chips etc... between a large battery and a huge FullHD display, they will run hot, especially when charging, using LTE or heavy graphics usage.
It's normal, but what isn't normal is if it heats while doing absolutely nothing, go to Settings -More tab -Battery, and see what's eating battery.