Thermal conductivity of a CuCrZr alloy containing of 0.71% of Cr and 0.23% of Zr was measured in the temperature interval from 5 K to 300 K. A method utilizing the measurement of thermal conductivity integral of a sample was verified and applied. Measurements of thermal conductivity, electrical resistivity at 4.2 K and 295 K and of Brinell hardness were performed on solution annealed, precipitation hardened and “as received” materials. The CuCrZr alloy was found to be applicable where high mechanical properties together with high and stable thermal conductivity are required. The possibility to predict the thermal conductivity of precipitation hardened copper alloys from the electrical properties even if the RRR values are lower than 10 was verified at RRR = 5.