A control strategy for supply fans in constant-volume heating, ventilating, and air-conditioning (HVAC) systems that reduces the speed of the fan at part-load conditions is provided. The invention consists of a constant-volume HVAC system, wireless discharge air temperature sensors, wireless hot source and cold source temperature sensors, and a wireless controller coupled to a fan modulation device. The controller includes a finite state machine that switches between a high-temperature control mode and a low-temperature control mode. The controller also includes a calculator that calculates a high temperature setpoint and a low temperature setpoint as a function of the hot source and cold source temperatures. In high temperature control mode, the controller compares the maximum discharge air temperature with the high temperature setpoint, and it commands the fan modulating device so that the maximum discharge air temperature remains close to the high temperature setpoint. In low temperature control mode, the controller compares the minimum discharge air temperature with the low temperature setpoint, and it commands the fan modulating device so that the minimum discharge air temperature remains close to the low temperature setpoint. Alternatively, the controller includes a calculator that computes a largest load as a function of previous fan command, discharge air temperatures, and readings from wireless zone temperature sensors. The controller increases the speed of the fan as the largest load increases, and reduces the speed of the fan as the largest load decreases.