Has your iPad been jailbroken?
Unauthorized modification of iOS can cause security vulnerabilities, instability, shortened battery life, and other issues
I have the exact same problem.
The phone keeps randomly draining the battery and getting crazy hot!
Last night I had 42% remaining two minutes later the phone had got very hot and the phone was off and wouldn't turn back on. I plugged it in and got the flat battery start up screen.
I've only had this since iOS6.1.3.