A system includes a variable-capacity compressor operable at a first capacity and at a second capacity that is higher than the first capacity and an outdoor-air-temperature sensor. A control module receives a demand signal from a thermostat and operates the variable-capacity compressor in a first mode when communication with the outdoor-air-temperature sensor has not been interrupted and in a fault mode when communication with the outdoor-air-temperature sensor has been interrupted. In the first mode, the control module switches the variable-capacity compressor between the first capacity and the second capacity based on the demand signal and the outdoor-air-temperature data. In the fault mode, the control module operates the variable-capacity compressor by operating the variable-capacity compressor at at least one of the first capacity and the second capacity based on the demand signal.