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 wakeup, which results unable to attend the call.
Even after giving the feedback through beta program the company doesn’t care to fix the issues. I they may also rectify or even understand the issues properly. Maybe that’s thereason they were forced to slash the price for 4s. In one way they are trying to lure out the customers with this price slashing and thus to sell out all those crapy devices which are already in their stock. It is not meomary card slot .it has 3.5 screen .it can only connet apple to apple .it has no bluetooth connective.