I have heard that the battery can become very hot when playing games. Some officianado from an American Techo Forum advised people suffering from this to completely discharge the battery before re-charging it again, which, per him, solves the problem.
I don't know if this would be the answer for you, but it must be worth a try as it would do no harm. After all is said and done, there must be a lot of people out there who use their iPad too much and end up emptying the battery before recharging again, without causing a problem.