Is this enough for them to replace my iPhone or will they say something along the lines of "your battery life seems fine according to our diagnostic check so there's nothing we can do".
Yeah, it's hot..not just warm. You could hold your hand on the back and not get burned or anything, but it's almost as hot as the bottom of most laptops.
They'll likely look ay your phone's charging cycle history and install diagnostic software that will tell them more about how your phone is being affected in detail. For them to replace the phone on the spot, they'll need to see something really abnormal on the spot or in your phone's diagnostic logs.