A thermoelectric heat pump is a miniature solid state device used to pump small amounts of heat. Potential uses range from the cooling of electronic components to dorm size refrigerators. An ongoing study at the U.S. Naval Academy proposes to use a miniature thermoelectric heat pump to maintain a neutron dosimeter at near constant temperatures in order to obtain more accurate readings. Unfortunately, the coefficient of performance of the heat pump decreases rapidly with increasing temperature difference. The current study investigates the potential improvement in heat pump performance that can be obtained by cascading two or more heat pumps in series operation.