I had a similar problem and two hard resets later, i realized that the problem was the whatsapp application that seems incompatible with WP 8.1. If you have it installed, uninstall it and do a soft reset, that should easily see you do 1 day and a few hours per charge cycle.
Charging is good for me and the heating while charging is gone as well. Now the phone is cold most of the time and i keep wondering whether it is on really!
I am using a Lumia 1020, which is always on 3G with toast notifications for everything enabled and I get a full day and about 10 hours per charge.
I will only install whatsapp when a newer version compatible with WP8.1 comes out