A system for controlling an air conditioning unit, the air conditioning unit including a variable speed compressor, the system comprising: a thermostat unit including: a temperature sensor measuring an ambient temperature of an environmentally controlled space; a switching module controlling conduction of a signal over a controlled time interval; characterized by a thermostat processing module determining a temperature difference between the ambient temperature and a set temperature, processing the temperature difference between a range between T max and -T max, determining a duty cycle corresponding to the temperature difference from the temperature difference divided by said T max times 50% plus 50% (EQ.4), and controlling the switching module in accordance with the duty cycle, the signal being electrically conducted during an activated time duration and electrically blocked during a deactivated time duration over a time period, the duty cycle specifying the activated time duration and the deactivated time duration; and a compressor controller unit including: a signal interface module monitoring the signal from the thermostat unit; and a compressor controller processing module determining the duty cycle from the signal, determining the temperature difference from the duty cycle, and determining an updated compressor speed from the temperature difference, and instructing the variable speed compressor to function at the updated compressor speed. a thermostat unit including: a temperature sensor measuring an ambient temperature of an environmentally controlled space; a switching module controlling conduction of a signal over a controlled time interval; characterized by a thermostat processing module determining a temperature difference between the ambient temperature and a set temperature, processing the temperature difference between a range between T max and -T max, determining a duty cycle corresponding to the temperature difference from the temperature difference divided by said T max times 50% plus 50% (EQ.4), and controlling the switching module in accordance with the duty cycle, the signal being electrically conducted during an activated time duration and electrically blocked during a deactivated time duration over a time period, the duty cycle specifying the activated time duration and the deactivated time duration; and a compressor controller unit including: a signal interface module monitoring the signal from the thermostat unit; and a compressor controller processing module determining the duty cycle from the signal, determining the temperature difference from the duty cycle, and determining an updated compressor speed from the temperature difference, and instructing the variable speed compressor to function at the updated compressor speed. a temperature sensor measuring an ambient temperature of an environmentally controlled space; a switching module controlling conduction of a signal over a controlled time interval; characterized by a thermostat processing module determining a temperature difference between the ambient temperature and a set temperature, processing the temperature difference between a range between T max and -T max, determining a duty cycle corresponding to the temperature difference from the temperature difference divided by said T max times 50% plus 50% (EQ.4), and controlling the switching module in accordance with the duty cycle, the signal being electrically conducted during an activated time duration and electrically blocked during a deactivated time duration over a time period, the duty cycle specifying the activated time duration and the deactivated time duration; and a compressor controller unit including: a signal interface module monitoring the signal from the thermostat unit; and a compressor controller processing module determining the duty cycle from the signal, determining the temperature difference from the duty cycle, and determining an updated compressor speed from the temperature difference, and instructing the variable speed compressor to function at the updated compressor speed. a signal interface module monitoring the signal from the thermostat unit; and a compressor controller processing module determining the duty cycle from the signal, determining the temperature difference from the duty cycle, and determining an updated compressor speed from the temperature difference, and instructing the variable speed compressor to function at the updated compressor speed.