A temperature control method includes obtaining, by a controller, a space temperature value, a space temperature set point, a discharge air temperature value, and a discharge air temperature set point. The method further includes determining a compressor speed using a first PI loop based on the space temperature set point and the space temperature value, and determining a supply fan speed using a second PI loop based on the discharge air temperature set point and the discharge air temperature value. The temperature control method further includes outputting a first control signal that controls the speed of a variable speed compressor based on the determination of whether the compressor speed is within the compressor operation range and a second control signal to control the speed of a variable speed supply fan based on the determination of whether the supply fan speed is within the supply fan operation range.