I had the same promoem with mu S4, always hot, fast battery drain. Tried all options, change battery with new one, same problem, after that i had one full battery in my pocket for quick swap (that was my favorite, hate non swapable phones). Tried fress install, feom recovery menu, same problem. Root my phone for uninstalling s-health s-memo s.s.s.s.s.s and all apps one by one, little longer battery life but nothing huge. Facebook and messenger has biggest hit on battery performance. I don’t have possibilities for contact Samsung but I get my things in my hand and start experimenting . Get another S4 and start swapping, swap mainboard, cameras, all parts one by one and nothing changes. Next step was system, flashed new android revision, older ones, beta ones, had some data inprovment, some sistems give few hours less or more. Tryed to write personal android based on samsung bootloader and system and that was main problem, I didn’t changed anything, after that I give away bought Iphone and let it go.
Last year I found my S4 in drawer and start test again but this time on basic android, not samsung one. Just plane android withou any app preinstalled or any modification, now I use S4 again as second phone but my battery life is 2-12 days based on usage. With stock samsung android it was 10-16 hours, that is huge difference, I didn’t find out what eating battery but if you dissable wifi, mobile data and gps your phone will be cold and battery life will hit 5+ days, something inside samsung android system use lot data transfer, I will love to find out what it is.