The development and characterization of new materials is of extreme importance in the design of cryogenic apparatus. Recently Versarien® PLC developed a technique capable of producing copper foam with controlled porosity and pore size. Such porous materials could be interesting for cryogenic heat exchangers as well as of special interest in some devices used in microgravity environments where a cryogenic liquid is confined by capillarity. In the present work, a system was developed to measure the thermal conductivity by the differential steady-state mode of four copper foam samples with porosity between 58% and 73%, within the temperatures range 20 - 260 K, using a 2 W @ 20 K cryocooler. Our measurements were validated using a copper control sample and by the estimation of the Lorenz number obtained from electrical resistivity measurements at room temperature. With these measurements, the Resistivity Residual Ratio and the tortuosity were obtained.