Thermoelectric heat pumps using parallel flow, crossflow, or counter-flow of the input and output fluid streams have been designed and built, but performance has been insensitive to flow arrangement due to the use of one-piece, essentially isothermal heat exchangers on the heated and cooled thermoelectric junctions. Thus, none of these designs have capitalized on the sensitivity of the thermoelectric coefficient of performance to the junctions temperature differences and the smaller temperature differences possible with the counter-flow arrangement. In the improved design, the thermoelectric heat pump is broken down into discrete sections which heat or cool the input fluid in stages. The system thus operates as several discrete heat pumps each doing only a small portion of the heat pumping without sacrificing the desired final outlet temperature. Thus, the junction temperature differentials for each thermoelectric unit in the system is less than that with conventional one-piece heat sink designs. Consequently, the coefficient of performance or "heat pump efficiency" of the sectioned system is significantly improved.