Abstract: The dehumidifier has a rotary bed 6 containing a thermally regenerable desiccant material, including a process segment 7 and a regeneration segment 8, and an air-to-air heat exchanger A having first and second heat-exchange channels A1 and A2. A process air channel 20 conducts process air through the process segment 7 of the rotary bed, through heat-exchange channel A1 of heat exchanger, to outlet 3. A cooling air channel 22 conducts cooling air from an external cooling air inlet 4a, through heat-exchange channel A2 of heat exchanger A to an exhaust air outlet 5a without passing through the rotary bed. The temperature of the return process air is controllable by a variable speed fan 12. A regeneration air channel 26 conducts air via heater box 9 through the regeneration segment 8 of the rotary bed, to exhaust air outlet 5b. The dehumidifier includes a second air-to-air heat exchanger B having first and second heat-exchange channels B1 and B2.