The heat index thermostat is an electronic, programmable thermostat having a microcontroller or microprocessor programmed to regulate the temperature of an enclosed space, such as a room or building. The thermostat has a user interface that permits the user to select a mode of operation and to enter a set temperature, and input terminals for receiving signals from relative humidity, indoor temperature, and other sensors. In a heat index mode of operation, the temperature is regulated by reference to a lookup table based on a heat index equation. The microcontroller uses the table inversely by using the set temperature as the heat index temperature, looking up the room temperature that would result in that heat index temperature given the measured relative humidity in the room. The thermostat then turns the cooling/heating unit on or off until the measured room temperature is equal to the temperature determined from the lookup table.