Thermal properties of metal matrix composite materials are becoming ever more relevant with the increasing demand for thermally efficient materials. In this work, the thermal conductivity and heat transfers at the interfaces of copper matrix composite materials reinforced with diamond particles (Cu/D) are discussed. The composite materials contain either ZrC or TiC interphases and exhibit, respectively, higher and lower thermal conductivities with respect to their pure Cu/D counterparts. These thermal conductivities are accounted to the presence of strong covalent bonds and increased relative densities. The role of these interphases is also discussed regarding the phonon transmission at the interfaces. (c) 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).