No changing the battery won’t fix that, not even changing the device. The have replaced my device under warranty condition, but still the issue persist.
As far as I could know that the 4s devices which are upgraded to iOS 9 ( even the brand new products which comes with pre-installed iOS 9) having the issues with battery- draining too fastly and heating while charging and sometimes using internet, lagged response and hanging issues- some devices facing issues like.
While call coming the display took more time than it’s supposed to be to wake up, which results unable to attend the call.