Okay, what "icon like it is dead" are you referring to? I was of the understanding you observed a temperature warning. If it is just the device turning off, then user troubleshooting steps are restart, reset, restore from backup, restore to factory, testing after each step. The phone feeling warm could indicate a process being stuck, and the restore should correct that. It would be unusual for a iPhone 6 series to have battery issues already, but not impossible. I would try the troubleshooting steps, and if that does not fix it, then make an appointment at the Genius Bar of the nearest Apple Store to have the device examined. Apple will explain your options.
Restart your iPhone, iPad, or iPod touch - Apple Support
Restore your device from an iCloud or iTunes backup - Apple Support.
Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support