Many heating, ventilation, air conditioning, and refrigeration systems operate using on/off controllers. A high and a low set point are selected above and below the desired temperature to command the refrigeration cycle to turn on or off when those temperatures are reached. In this study, exponential temperature correlations are used in a gray-box approach to provide information about the estimated mean temperature, average power consumption, and number of compressor starts per hour. Based on the governing equations and the heat balance of the system, a set of formulations is developed as a new analytical tool for the design of set points. It is discussed that for any specific application, the set point values can be properly selected to minimize the overall energy consumption subject to the design constraints. It is shown through an experimental study that the selection of the set points can affect the overall energy consumption by up to 49% for the same desired temperature. It is also shown that there is a further opportunity for increasing the energy efficiency by 6.6% using different high and low set point hysteresis values. The developed model can be used for designing and analyzing new systems. It can also be used for retrofitting existing units and achieving the highest energy efficiency subject to the design constraints. (C) 2015 Elsevier Ltd. All rights reserved.