Read Batteries - Maximizing Performance - Apple
"A normal battery is designed to retain up to 80% of its original capacity at 500 complete charge cycles when operating under normal conditions. The one-year warranty includes service coverage for a defective battery. If it is out of warranty, Apple offers battery service for a charge." --> iPhone Battery Repair & Replacement - Apple Support
If you really want it replaced, go to this web site for information about how to request battery service for your iPhone: iPhone Battery Repair & Replacement - Apple Support
Also read this article about keeping your iPhone, iPad, or iPod touch within acceptable operating temperatures - If your iPhone or iPad gets too hot or too cold - Apple Support
Having a device get warm while in use is to be expected.