Hello Angelo9402,
Welcome to Apple Support Communities! I understand that the screen on your new iPhone 11 shut down unexpectedly and would not turn back on for a few minutes. You've come to the right place for help.
If you're using your iPhone in a cold environment outside of acceptable temperature ranges, this can cause the device to power off in order to protect the battery:
Keeping iPhone, iPad, and iPod touch within acceptable operating temperatures - Apple Support
"Use iOS devices where the ambient temperature is between 0Âș and 35Âș C (32Âș to 95Âș F). Low- or high-temperature conditions might cause the device to change its behavior to regulate its temperature. Using an iOS device in very cold conditions outside of its operating range might temporarily shorten battery life and could cause the device to turn off."
You can also learn more about this behavior under the "Preventing unexpected shutdowns" section here:
iPhone Battery and Performance - Apple Support
While it's not the typical experience, an iOS device can become frozen due to a variety of factors. Forcing your device to restart following the "If your screen is black or frozen" section can help:
If your iPhone, iPad, or iPod touch won't turn on or is frozen - Apple Support
If neither scenario describes what you encountered, could you tell us more about what happened when you experienced this behavior? Did the iPhone seem to be frozen with the screen locked but powered on? Did the iPhone restart displaying either an Apple logo or spinning icon before powering on again?
Cheers!
