Infiltration of tool steels with copper is a suitable and cheap method to create dense parts using powder metallurgy. In this work, it is shown that the copper network that forms inside the steel skeleton during infiltration enhances the thermal conductivity of the resulting composite. The level of enhancement is dependent on the thermal conductivity of the copper phase and the volume fraction of copper. Multiple heat treatments of this composite revealed a strong dependency between the thermal conductivity of the composite and the solution state of Fe in the copper network. The latter is highly dependent on the heat-treated condition of the multi-phase material. Using infiltration, the thermal and electrical conductivity was increased from and from respectively, for aged steel-copper composite in comparison with original X245VCrMo9-4-4 steel. In addition, a model alloy that represents the copper-phase network in the composite was manufactured. By measuring both, the thermal conductivity of this model alloy and the bulk steel, and comparing it to the data for the composite, different models for calculating the overall conductivity of the composite are discussed.