The present invention is a technique for thermostatic control of a temperature modifying apparatus such as a heating unit or an air conditioning unit. This technique involves measuring the ambient temperature, generating an error signal based upon the difference between a set point temperature and the measured ambient temperature, operating the temperature modifying apparatus according to the error signal, and adjusting the set point temperature based upon the time history of the error signal. In accordance with the preferred embodiment of the present invention, the temperature modifying apparatus is operated during the next cycle interval with a duty cycle proportional to the error signal at the start of the cycle interval. In the preferred embodiment the set point is adjusted via an adjustment quantity which is increased if the difference between a desired temperature is of one sense decreased if the difference is of the opposite sense and maintained unchanged if the desired temperature equals the measured temperature, with the adjustment quantity maintained within a predetermined band.