iPhone 5 battery replacement issues

the iphone 5 I am working on, the old battery was so bloated (it belongs to my other half, & three weeks a month we're apart, so I didn't catch it happening) that it had pushed the display way out of the front of the phone & cracked the bezel. I gave her a spare iphone 5 of mine so I could work on this one.

(two years ago, her gen1 macbook 17" trackpad stopped working, acted like you were pressing it all the time. battery looked fine from underneath, but it had swollen out the top of its case & was pushing on the trackpad from underneath. still holding good charge all the while. that was an easy fix.... :-) )

so the phone came apart easy enough. I knew I wasn't going to get it all done in one go when I saw the bezel was broken- I'm waiting for a new one now- but I carried on & got the old battery out, without taking the display cabling out.

put the new battery in... got the temperature alarm. many many hard resets & reseating the battery cable, & the alert is still there.

is the new battery faulty?