My S4 started running very hot and draining the battery after I moved a few apps and a bunch of photos and video to the SD card.  I removed the apps but the problem continued.  I tried the factory reset and that didn't help.  When I unmount the SD card, the battery consumption and temperature are normal.  Now I only mount the SD card to show photos or something, and the S4 immediately heats up.  I have not yet tried to reformat the card or a different card.
I suspect that the OS is continuously reading the card when it is mounted, and the problem shows up when you add more content to the card.  It is almost surely a software issue.
Those of you with the heat/battery drain issue, please try unmounting your SD card to see if the problem resolves.  Yup, it's a workaround, but until the fault is found, it can't get fixed.
Regards,
- Just Gary