PURPOSE: To reduce the varying width of temperature in a room and permit to effect comfortable air-conditioning by equipping the device with a thermo-circuit having no temperature differential.

CONSTITUTION: The operation of a compressor 10 is maintained by an ON circuit 25 for at least predetermined time to increase the capacity of the compressor and when the compressor 10 is stopped once, the stoppage of operation of the compressor 10 is maintained by an OFF circuit 32 for at least a predetermined time to protect the compressor 10, thereafter, the operation of the compressor 10 is controlled by the thermo-circuit 19 having no temperature differential. According to this method, in case a temperature sensitive element is attached to a place whereat the convection of air does not exist and the change of the temperature is slow, the varying width of the temperature in the air- conditioned room becomes small and the comfortable air-conditioning may be effected.