I don't know if this is relevant to this issue but when I got my S4 I found out later it was actually a different version. There were 2 types of S4. There were slight differences. I remember the one I have didnt have either 4g or that other high speed method on.
Also it was always 'dodgy' when it came to charging it. The charger adapter that you plug in to the mains has never worked properly. It just doesn't charge it. The only way I've been charging it as been via usb cables to my computer. I don't know if this is connected but just as all these stories started coming out I was charging my phone like usual at the computer, like I've done many times before. But now there was no charge and the phone was very hot. I took it out of the case I had it in (always had it in the case for years and never a problem), and I did buy a new battery to replace it as I'd heard it could be the battery. But since then its started charging fine again and no heat.
I also noticed if I put it in an open drawer of my bedside table, so its reachable if anyone calls. If it drops further inside the open drawer it got hot. I'm not sure why. Unless it was struggling to get a signal and thats why? I'd not noticed that before. I haven't re-tested the drawer position since the phone stopped getting hot again, and I still have the spare battery sat here. I never used it.