The main current of publication is focused around the issues and problems associated with the formation of composite materials with Cu matrix and reinforcing phases in the various carbon nanoforms. The core of the research has been focused on thermal conductivity of these composites types. This parameter globally reflects the state of the structure, quality of raw materials and the technology used during the formation of composite materials. Vanishingly low affinity of copper for carbon, multilayered forms of graphene, the existence of critical values of graphene volume in the composite are not conducive to the classic procedures of composites designing. As a result, the expected, significant increase in thermal conductivity of composites is not greater than for pure copper matrix. Present paper especially includes: (i) data of obtaining procedure of copper/graphene mixtures, (ii) data of sintering process, (iii) the results of structure investigations and of thermal properties. Structural analysis revealed the homogenous distribution of graphene in copper matrix, the thermal analysis indicate the existence of carbon phase critical concentration, where improvement of thermal diffusivity to pure copper can occur.