A thermostat comprising: a wireless communication circuit (404, 1004) configured to receive temperature readings from a remote temperature sensor (102, 920); a processor (402, 1002) configured to operate in a plurality of modes, wherein the plurality of modes comprises: a first mode; and a second mode, wherein the processor (402, 1002) uses more average power when operating in the second mode than when operating in the first mode; a memory comprising instructions that, when executed by the processor (402, 1002), cause the processor (402, 1002) to: repeatedly transition between operating in the first mode and operating in the second mode, wherein: transitions from operating in the first mode to operating in the second mode are caused at least in part by an expiration of a first time interval (908, 1114); and the wireless communication circuit (404, 1004) is configured to receive one or more of the temperature readings from the remote temperature sensor (102, 920) while the processor (402, 1002) is operating in the second mode; and adjust (1308, 1312) a length of the first time interval (908, 1114) based at least in part on an estimate of how fast the temperature readings from the remote temperature sensor (102, 920) are approaching a threshold temperature (1120, 1122), wherein the threshold temperature comprises an upper or lower boundary of a maintenance band around a setpoint temperature. a wireless communication circuit (404, 1004) configured to receive temperature readings from a remote temperature sensor (102, 920); a processor (402, 1002) configured to operate in a plurality of modes, wherein the plurality of modes comprises: a first mode; and a second mode, wherein the processor (402, 1002) uses more average power when operating in the second mode than when operating in the first mode; a first mode; and a second mode, wherein the processor (402, 1002) uses more average power when operating in the second mode than when operating in the first mode; a memory comprising instructions that, when executed by the processor (402, 1002), cause the processor (402, 1002) to: repeatedly transition between operating in the first mode and operating in the second mode, wherein: transitions from operating in the first mode to operating in the second mode are caused at least in part by an expiration of a first time interval (908, 1114); and the wireless communication circuit (404, 1004) is configured to receive one or more of the temperature readings from the remote temperature sensor (102, 920) while the processor (402, 1002) is operating in the second mode; and adjust (1308, 1312) a length of the first time interval (908, 1114) based at least in part on an estimate of how fast the temperature readings from the remote temperature sensor (102, 920) are approaching a threshold temperature (1120, 1122), wherein the threshold temperature comprises an upper or lower boundary of a maintenance band around a setpoint temperature. repeatedly transition between operating in the first mode and operating in the second mode, wherein: transitions from operating in the first mode to operating in the second mode are caused at least in part by an expiration of a first time interval (908, 1114); and the wireless communication circuit (404, 1004) is configured to receive one or more of the temperature readings from the remote temperature sensor (102, 920) while the processor (402, 1002) is operating in the second mode; and transitions from operating in the first mode to operating in the second mode are caused at least in part by an expiration of a first time interval (908, 1114); and the wireless communication circuit (404, 1004) is configured to receive one or more of the temperature readings from the remote temperature sensor (102, 920) while the processor (402, 1002) is operating in the second mode; and adjust (1308, 1312) a length of the first time interval (908, 1114) based at least in part on an estimate of how fast the temperature readings from the remote temperature sensor (102, 920) are approaching a threshold temperature (1120, 1122), wherein the threshold temperature comprises an upper or lower boundary of a maintenance band around a setpoint temperature.