I bought a house with a Nest thermostat, and while I would never have purchased that expensive of a thermostat for a rental, I left it installed, rather than replacing it with a cheap Honeywell thermostat from Home Depot. BIG MISTAKE!
Once the wifi got disconnected when the prior owners moved out, the thermostat went on strike. No heat meant that plumbing froze and water damage occurred to the oak floors. Think Nest is expensive? That made it infinitely worse.
A similar thing happened recently, the tenants got a new wifi router. They disconnected the old router, once setting up the new router, they didn’t think of re-connecting the thermostat by entering the new wifi password. Nest went back on strike. No harm done, but the same symptoms occurred. Nest didn’t do its job until its addiction to wifi was sated.
My opinion as a former software analyst is that the thermostat should perform all its core functions regardless of internet status. We all know that heavy snow and other inclement weather can contribute to internet outages. However, this doesn’t appear how this version of a Nest thermostat operates. Buyer beware!