Typically the nest learning thermostat will remain operational for one to two hours during a blackout before it shuts off. Step 1 turn your thermostat to cool and on during the warmer months after a power outage.

Nest Learning Thermostat Austin Independence Title
Nest thermostat power outage. Smart thermostats have two important jobs. Follow these steps if your nest thermostat has been previously connected to your wi fi network but disconnects repeatedly or you see that its offline in the nest app or on the thermostat display. When power returns it could take another hour before power to the unit is operating properly. Be a thermostat and be online so when the servers go down and that feature is lost its easy to feel angry and frustrated. The battery voltage should be the first number you. Looks like lots of others with same issue searching twitter for nest offline.
At kingofframpton at googlenest i see you had an outage but are now saying its back online. On the thermostat go to settings technical info power. Ideally during power outages the nest thermostat would merely function for one to two hours on battery backup. You can adjust the temperature lower in order to jump start the air conditioning. This will reset your thermostat in the warmer months during the winter months you will need to follow a few more steps. When power is restored your settings will remain intact.
When the battery completely drains the thermostat isnt usable. Frequent outages make it difficult to use the thermostat the way most people want to. If the nests battery level gets below 36v it will stop connecting to your wi fi. This winter saw a series of frustrating server outages for smart thermostat owners particularly nest and ecobee. My nest thermostat says online ive restarted but the app still says its offline. Remotely through an app.
If you are new to this device and havent been in a situation where a thermostat had completely gone out of charge then you must know that after power restoration it will typically take an hour to back to its proper working state.