Lots of little tiny cheap ESP8266 based systems with DS18S20 temp sensors all over your house, telling you far more than just a single Nest thermostat could tell you.
Look into low power sleep modes, so that it can run for a very long time, waking up at some interval to take a quick temperature measurement, report it, then go back to sleep. While you're at it, have it confirm its battery level and report that too if the battery is low.
Look into low power sleep modes, so that it can run for a very long time, waking up at some interval to take a quick temperature measurement, report it, then go back to sleep. While you're at it, have it confirm its battery level and report that too if the battery is low.