Do not attempt it with a solder iron. If you have the gsm version I guarantee your going to dislodge one of the parralelle resistors that are placed directly in front of the center pins. A heat gun will also melt the plastic on the connector preventing the male end of your battery from properly fitting. Here is a painfully simple trick I didn't discover until I destroyed a logic board that's almost impossible to screw up. Pick up a circuit writer conductive pin from radio shack or online. Get some 91% isopropyln. Your also going to need a pair of tweezers and some cotton tips.
If the connector is already removed you'll need to make sure each copper trace for each pin is exposed. Hopefully you still have all 4 pins in tact and undamaged.
Throw the connector in a little cup of iso while you clean the area where the battery connects. Be generous on the iso. If you touch anything metal with your fingers it must be 're cleaned with iso and a q tip.
Get a little practice with the conductive pin so you understand how it flows.
Grab the battery connector with a pair of tweezers once the iso has dried and apply conductive paste to each pin individually.
Like wise also apply conductive paste to each pin on the motherboard side.
The great thing is that if you mess up, the conductive paste can be completely removed and reapplied as this stuff takes 24 hours to dry.
Once you have tinned both sides with paste gently place the connector onto The board aligning each pin separately.
If you are happy with the alignment make sure there is no remaining
paste shorting any pins together. Carefully inspect the sourrounding areas of the connector ensuring no other chips ar eshorted together with paste you may have dropped. Let the conductive paste dry for 24 hours.
Once dried I like to use some epoxy on both plastic sides of the connector. As the paste is not as strong as solder.
At the same time I also apply additional paste to each pin a second time after cleaning