The diploma thesis addresses the thermoelectric heat pump for the purpose of cooling or heating the air. It describes the thermodynamic basics of humid air and operation of the thermoelectric heat pump. Mathematical model for dimensioning a heat exchanger, which would allow simultaneous cooling and heating, is presented. On the basis of the mathematical model heat exchanger was constructed along with the measuring track, which analyzes heat exchanger's performance through its thermal characteristics. An experiment, which enabled the verification of the theoretical model and the actual operation of the heat pump in real environment was realized.