iPhone 5s hot from charge and won't start
phone was plugged in for charging. After a while I checked it and it was extremely hot. I unplugged it and now it won't start.
iPhone 5, iOS 8.1.1
Did you already try to force restart the phone by holding the sleep and home button for about 10sec, until the Apple logo comes back again? You will not lose data.
More troubleshooting steps can be found in this article:
If your iPhone, iPad, doesn't respond or won't turn on - Apple Support