Chosen Solution
The phone is getting very warm and discharging rapidly after new battery install.
What was wrong with the previous battery? You may want to consider doing an iTunes backup of the phone, restore it then restore from the iTunes backup that you made and see if that helps with the rapid battery drain issue. Note that you can check battery health either via the Battery Life app on iOS, Coconutbattery app on Mac OS X or 3UTools on Windows.
