The best way to check this is always going to be to completely wipe the phone and setup as new. It doesn;t have to be permanently, but it's an easy diagnostic. Restore the phone, don't install anything if you can help it, and just give it a day or two. If it's a hardware issue, you will see the exact same thing happening with a completely wiped phone.
You can either backup to icloud or your computer so that when the time comes you can get back everything you had before wiping. The idea behind wiping is leaving the phone factory dead stock for a while. Nobody can tell you it's your apps or your backup draining your battery if it's draining with a clean stock OS instal.