Dear, As per your problem, it seems to end at Battery issue. you are saying that your battery is draining faster. Also the cell is getting hot. So, I will strongly recommend you to get the mobile checked . Actually the problem of getting hot occurs when there is any issue in the connection between phone and the battery or the circuit is faulty. So in either case, you should contact to your nearest Service center.
Normally Samsung S4 gives a battery backup of 17 hours ( talk time backup claimed by company). Hence it is really an issue to get resolved.