This paper demonstrates the existence of an optimal on/off sequence for operating a household refrigerator that accumulates ice on its evaporator coils. Experimentally it is shown that the rate of ice formation is constant in time. The optimal (intermittent) regime of operation determined in this paper minimizes the power required by the refrigerator, maintains the prescribed temperature of the cold space, and removes intermittently the ice layer. The second part of the paper proves that a similar strategy can be used for dealing with fouling in heat exchangers, i.e. for maximizing the power output of a power plant that is diminished by the formation of scale on its heat exchanger surfaces. These optimal on/off sequences of operation for refrigerators and power plants are proven based on pure heat transfer and themodynamics grounds. The refrigerator and power plant models employed are the simplest models possible. Consequently, the optimal on/off sequences demonstrated in this paper are fundamental features that will be present (and deserve to be identified and exploited) in the design of actual refrigerators and power plants, no matter how complicated these designs may be.