This paper presents the thermal behavior of ZrB2 skeletal material (38% porosity) infiltrated with pure Cu or CuCrZr alloy. Gas-assisted pressure infiltration technology was used to prepare the composites. Thermal diffusivity, density and specific heat measurements were used to calculate the thermal conductivity—the room temperature values of the Cu-ZrB2 and the CuCrZr-ZrB2 material were 157 W m−1 K−1 and 146 W m−1 K−1, respectively, and they decreased with increasing temperature. Analysis of the results showed significant influence of the interface on the thermal conductivity of the CuCrZr-ZrB2 composite. The results indicate that the improved interfacial conductivity was formed due to the presence of the Zr in both the copper alloy and the ceramic skeleton. During infiltration, Zr atoms diffused from the liquid metal to the interface between the metal and the matrix. Here, they created a layer that had metal-related properties. The layer improved wettability of the interface and at the same time the thermal conductivity of the whole composite. The values were compared with the data of the Cu–graphite composite made by the powder metallurgical route where heat transfer through the interface approaches zero. Obtained experimental data were analyzed using the Differential Effective Media (DEM) technique, showing high thermal conductance of the interface between the CuCrZr metal matrix and ceramic skeleton.