My Lumia 920 battery last only 1 day without heavy use. Full in the morning, died (turned off) at around 10pm. Defective battery?

I noticed the phone heats up (at the back) when i play with it for a few minutes. Same case when i'm charging it. The heat is noticeable, not like the residual heat when u hold some thing for some time.

My yellow lumia 920 is a defective unit, confirmed by nokia themselves. bought for 2 days. now they tell me to wait at least 2 weeks for them to order a new lcd to replace mine. Just 2 days and they tell me they're not going to replace me with a new phone. damn dissapointed. not helpful at all.
Waited at the Nokia Care Amcorp Mall ( they say its the main branch ) for one whole hour and a half and the person in charge, Kelvin is not at all helpful. Just showing the none of my business face. And nokia the gardens. Same thing.