Strange battery issue with iPhone 6

I bought an iPhone 6 on eBay that was listed with a charge problem.

You can see the 'red bar' charging screen with the black background when it's on charge, but it doesn't go the Apple logo.

I read online to heat it a bit awhile charging to get it past the charging screen, so I put in on a radiator for a minute and it went to the Apple logo and started charging to 100%.

I downloaded the Battery Life App and it stated that the battery was 100% good with no wear at all. I then updated to the latest IOS.

The phone drained to 0% charge within 4 hours. I only used the phone to refresh a forum site a few times during that 4 hours.

I had to do the radiator trick to get it past the charging screen again. Same problem. Battery dead in less than 4 hours, yet the Battery Life App states that the battery is fine.