The analysis of cooling of a binary high T-c superconductor (HTS) 20 kA current lead (CL) operating between 4.5 and 300 K is carried out. We assume that the HTS module is conduction cooled, whereas the cold end of the copper heat exchanger (HEX) is immersed in a liquid nitrogen bath under normal pressure, and the rest of the HEX part is cooled by the nitrogen vapor. The ideal refrigerator power required to cool the whole HTS CL is calculated for different values of input parameters, and the thermodynamic optimization of the HTS CL is performed. In addition, the analysis of cooling of the same HTS CL operating at currents lower than nominal is carried out. The studied case is compared with the standard cooling option in which the HEX part is cooled with a flow of gaseous helium.