A thermostat system according to the invention includes: a central control device (typically a programmable thermostat with a processor having: a CPU, real time clock and a memory for storing a control program and data information), multiple rooms comprising a conditioned space, environmental control equipment, and multiple environmental sensors capable of sensing an environmental condition (such as temperature, humidity, or other condition). The sensors are associated with transmission means, which control transmission of sensor signals, and occupancy sensors. Each sensor measures a local environmental condition. Occupancy sensors comprise infrared or other motion sensors, light detection sensors, door opening sensors, and other such sensors that detect the presence of humans in a room of the conditioned space where its associated sensor is located. Space conditioning equipment is activated by comparison of a setpoint to a control value averaged from values of environmental conditions in occupied rooms.