Meet the Nest Learning Thermostat. It learns what temperatures you like, turns itself down when you’re away and connects to your phone. It has a big, sharp display. And it’s proven to help save energy. In independent studies, the Nest Thermostat saved an average of 10percent to 12percent on heating bills and 15percent on cooling bills. We’ve estimated average savings of $131 to $145 a year. Color: Black.