Communication between the various elements of HVAC systems is effected by means of low-cost, low-power, narrow-band AM SAW-stabilized transmitters 21, 27, 39, 86 and receivers 18, 28, 47, 89. A residential embodiment (FIG. 1) transmits temperature information from each room of the house to a master control 24, which is used to control the HVAC demand and to control the damper in the corresponding room. In a first commercial building embodiment (FIGS. 2 and 3), thermostat/transceiver 61-66 assemblies transmit not only demand and control information from the corresponding thermostat 78 (with switches), but relay information transmitted from other thermostat/transceiver assemblies, whereby messages are retransmitted from one floor to the next to overcome the high attenuation of commercial building construction in reaching rooftop HVAC systems 71-76. In a second commercial building embodiment (FIG. 4), messages are transmitted from a thermostat/transceiver assembly 92 in each floor to a relaying transceiver assembly 96 in a stairwell, the transmissions to rooftop units 93, 97 being made with little attenuation through the stairwell and the roof. Message protocols with or without acknowledgement may be used. Relative humidity and CO.sub.2 level may be controlled as well as temperature.