iOS 6.1.3 iPad (4th Gen) battery?

I have a white 4th generation 64GB wi-fi iPad. I held off as long as I could on updating the firmare to the latest (iOS 6.1.3?). I have noticed a few improvements over the stock iOS 6 firmware. However, i have also had a major problem with it. I don't know if it is a hardware problem or a firmware problem (maybe both?).

I did the firmware update using iTunes on my PC. To be on the safe side, I reset my PC, cleared out junk/temp files from my PC using CCleaner. I disabled my Anti-Virus, and also disabled my firewall. I made certain no other applications were running. I did the update by erasing my iPad and chose to set it up as a new iPad.

After the update to iOS 6.1.3, I have had 2 major issues. First, the battery is no longer holding a good charge. The battery is draining a lot faster than it ever did before I did the update. Secondly, when using the wall charger (which to be safe is plugged into a surge protector), I thought I was hallucinating things but my iPad has started getting very hot while charging. I tried charging it at various different locations, and have had the same result. Has anyone else had any known issues with 6.1.3 with either massive battery drain or the iPad itself overheating?

I contacted Apple and expressed my issue. Unfortunately, i live in a small town in the middle of Indiana. I don't have access to public transportation and the closest actual official Apple store is over an hour drive from where i live. I am also permanently disabled and on a very limited income. So I don't have the extra cash to not only pay to ship my iPad to Apple. Considering how expensive an iPad is, I could and would not even consider shipping it without both shipping insurance, a tracking number, and the requirement of a signature to verify it arrived at Apple. Unfortunately, I purchased it over 30 days ago, so I cannot just return it to the store I bought it at (Best Buy) to exchange it for a new one.

Does anyone have any potential good working suggestions or solutions to attempt to address the battery issues i am having? If not, am I stuck with just hoping it doesn't catch fire and safe for a few months to afford the over priced shipping cost to send it to Apple to be repaired?