iPhone 5s overheating, battery drain, takes too long to charge

I've seen this issue on the forum and elsewhere but still looking for a solution. The basics: version 7.0.2 (11A501), Carrier is EE, backed up from my iPhone 5.

So when I first purchased the phone I used the phone for a 30 min call and it used 40% of my battery, it takes about 2 hours to charge 5%, the phone gets abnormally hot (no over heating message). I went to the Genius Bar they said the battery was perfect, assumed its the iOS. They did a factory reset. Instead of going straight home to sync I used it as a "new phone" for 48 hours (little usage, no apps) and it seemed just fine. This morning I did the factory reset per their instructions and it's doing the same thing again. Any bright ideas? I tried turning off wifi for awhile, turning off apps that use Location Services. If I return it and stay with the iPhone 5, will I have the same issues with iOS7? Thanks for your help.