Home heating systems often have a significant thermal inertia, as homes stay warm after the heating is turned off for significant periods of time. We present the EarlyOff concept, whereby home heating can be predictively turned off in advance of occupants’ departure, using this inertia to keep the house warm while saving energy. We use a previously gathered data set of real-time heating, gas, and occupancy readings from five houses and conduct a data-driven analysis of potential energy savings. Using an “oracle” predicting actual departure events, we show an upper bound savings of 4–12% of the gas used over the whole study period by applying EarlyOff. Using a real predictor which makes use of historical occupancy probabilities, we show savings of 1–8% of gas use.