Apple Cinema Display Overcharges my Macbook Pro 13" (2012)

In my mac setup, I have the apple cinema display 24" on top of my desk while the laptop is in the desk cabinet. Since i want my laptop to be closed, the monitor only works if the magsafe connector is also plugged into the laptop. My concern is that the battery will overcharge. I contacted the apple store via chat and they said it wouldn't. However, after about 2 hours of usage with the laptop beign fully charged, the laptop started overheating so i disconnected the monitor form the lapotp. I figured out tat the battery had dropped half of its battery life according to the battery icon on the top of the laptop. Is there anyway I can connect my laptop to the moinotr without overcharging it in anyway? I also tried mirro displays, but the resolution is too bad. Thank you guys for your help.