iPhone 6s completely unresponsive

My 16gb iPhone 6s became completely unresponsive yesterday after becoming very warm to the touch, not just the touch button but the whole phone. I tried doing a hard reset and nothing happened. I then tried to do a factory reset through iTunes and I kept getting error codes 4013 or 4005 essentially saying the phone was unable to complete the restore. It would go through the "extracting software" then "waiting for iPhone" but get hung up there and prompt me with an error code. This is actually my second iPhone 6s I've had the exact same problem with. My laptop is running the most current version os OS X and my version of iTunes is up to date as well. I contacted apple support and they extracted the logs from my laptop to see what is causing it but they will not be able to get back to me for 1-3 days. Any suggestions? I know the phone is still under warranty so I can bring it back in and request a new one, I've had it less than a week. When I press the on/off button I sometimes see the black screen with lights in the back, although the pattern is not consistent.