Threat of Battery perfromance and Heating

Last week I have bought a Brand New Nikon D5200. I have a threat that my battery is not performing well and I am also experiencing a little heat on back of body. 2 days back I attended an event and used the camera to capture the snaps, battery was full charged but I could have took only 180 approx photographs and battery drained completely. It was a complete night shooting and all the snaps taken at ISO2000; shutter speed - 1/80; using 55-200 zoom lens. File format was Raw. Approx after an hour of session Post the session I recharged the battery for half an hour and I was watching photographs on the LCD and I felt that it was getting heated. I Hope this is normal and nothing to get worried about it. Please suggest.

Welcome to the forum,there are a few things to consider,if you where viewing the images during and in between taking that would reduce the amount of pictures you could take,when reviewing later its possible there could be some heat build up from continues use of the lcd but i wouldn't expect much.
The other possibility is your battery needs a few charge and use cycles before reaching its optimum performance,the lcd will use your battery up,especially i believe if you have it too bright.

What Mikew said ^^^ Also along the same lines, if using Live View the battery will drain much faster than using the viewfinder while taking snaps.

plus you may want to look at buying a spare battery, not if yours is faulty but so you never run out while shooting, i know i have about a week of normal shooting on mine, but i carry the spare fully charged at most times, you never know.