From nest website: If the room temperature drops below the set Safety Temperature, your Nest Thermostat will automatically start heating. You'll receive a push notification on your phone or tablet, as well as a message in the Nest app. Once the temperature has returned to a normal level, another notification will let you know.
Important: Notifications about Safety Temperatures rely on an active Wi-Fi and Internet connection in your home at the time of the notification. If your Wi-Fi network is down when the Safety Temperature is reached, you will not receive the notification. Your thermostat will continue to heat while your home Wi-Fi network is offline.