A wire-cut electric discharge machine has a cooling device for cooling the machining fluid. A controller for controlling the cooling operation of the cooling device controls the machining fluid temperature by automatically switching, depending on the relationship between the ambient temperature of the wire-cut electric discharge machine and the temperature of the machining fluid, between a fixed temperature control mode in which the machining fluid temperature is maintained at a preset value and a differential temperature control mode in which the machining fluid temperature follows the ambient temperature to limit the difference between the machining fluid temperature and the ambient temperature to a preset range.