There is absolutely nothing wrong with your battery, and nothing wrong with the charger. At least, there wasn't before you got the battery HOT... Now, there might be a little loss of capacity... Running the plane on the ground for extended periods of time is BAD for the battery and motor. Keep static runs to 30 seconds, or preferably LESS

You simply fell for the myth that just because the battery is a LiPoly, it will magically make you plane fly for some ungodly length of time. Time for a little myth busting:

The mAh rating of the battery, not its chemistry, is what determines how long the plane will fly. mAh is mAh, no matter what kind of battery it is. If you get 13 minutes from a 1500mAh NiMH pack, you will get 13 minutes from a 1500mAh LiPoly pack of the same voltage.

LiPolys have an advantage in that you can pack five times as much capacity into the same space and weight as a NiCd, or about three times as much as a NiMH. On a plane like the Dandy Sport, you can expect about 5-6 minutes of full-throttle flying from a typical 650-720mAh NiMH pack. 13+ minutes, running static on the ground tells me that your battery is working fine. The heat buildup will make the motor draw more current, and make the battery less efficient. If you were flying, you can easily get 13+ minutes at full throttle. Using some throttle management, that is, only going to full throttle when you really need to, you could probably fly for 20+. Flying at the lowest possible setting, you could probably fly for 30 minutes or more.

Hobbico's MkII charger is conservative, and that is not a bad thing. You do not want to overcharge these cells. The pack was probably at 85-90% full, so your flying times would be much longer if it were fully charged.