I tried as I have replaced a number of other soldered ports. This seems permanently adhered with some kind of enamel. Not to mention two rows of contacts, one in front and on top of the other. No idea how to get it off safely.
So I just had this problem. Tried new battery, same issue. But when I completely reassembled the phone (I was testing phone after screen replacement so I didn't have it all put back together when I was having this problem) everything charged fine. No low temp issue. Something on the loudspeaker and other parts seem to cause problems if they are not connected. Hope you have the same problem.
I think you missed the step of removing the back and accidentally put in the slide for prying off the screen instead.