Battery won't hold a full charge
batteries don't have a life forever. And no one can predict the life time of a battery.
So many factors influence the lifetime. But if it is draining very fast, this mostly means it has reached the end of life. If the camera does not get excessive hot, it has nothing to do with the camera. It is just you need a new battery.
To keep a battery in shape for a longer time you should charge it also when the camera is not used. Like at least 4 times a year. Always charge the battery a day before you plan to use it. Don't over charge, like charging it every day. Don't leave it in the bright sun or on a hot place.
A new battery, should be charged and discharged a few times, before it gets a full charge.
The "New" battery you bought, could be in stock for a long time. Special when you could buy it very cheap.
Perhaps in a few days you say, he the battery works fine now. But if you did charge it 3 or more times and it still does not hold a charge. send the battery back (I hope you bought one with warranty)