A model of the behaviour of a two-stage semiconductor thermoelectric heat-pump with external heat transfer is devised. Performance of the heat-pump, assuming Newton's beat-transfer law, is analyzed using the combination of finite-time thermodynamics and non-equilibrium thermodynamics. The analytical formula describing the heating load versus working electric-current, and the coefficient of performance (COP) versus working electric-current are derived. For the fixed total number of thermoelectric elements, the ratio of number of thermoelectric elements of the top stage to the total number of thermoelectric elements is also optimized for maximizing the heating load and the COP of the thermoelectric heat-pump. The effects of design factors on the performance are analyzed. (c) 2007 Elsevier Ltd. All rights reserved.