Cutting tools made of polycrystalline diamond (PCD) are used for machining of aluminum alloys, fiber-reinforced plastics and wood. Compared to cemented carbide tools with geometrically defined cutting edges PCD tools offer significant advantages with respect to tool life. High demands regarding the cutting edge roughness and the quality of the rake and the flank face usually require a grinding process with diamond grinding wheels. The PCD grinding process, however, is characterized by low material removal rates and high grinding wheel wear. The material removal rate and the grinding wheel wear, in turn, highly depend on the process state variables process force and process temperature. However, the relationship between these process state variables and the process input variables is largely unknown. This work provides a contribution to the closure of this knowledge gap by means of an adapted friction law. A single-grain friction test stand using the pin-disk principle was developed, which enables a measurement of the friction force and the contact zone temperature for normal forces and relative speeds that are common in PCD grinding. During the experiments, the specification of the PCD disc, the cross-sectional area of the friction sample made of monocrystalline diamond as well as the process parameters normal force and relative speed were varied. In addition, the tests were carried out without lubrication as well as with a minimum lubrication. A high correlation between the contact force and the coefficient of friction was determined. This relationship was mathematically formulated in a friction law. In addition, a direct influence of the contact force and the relative velocity on the contact zone temperature was identified. The knowledge gained leads to an improved understanding of the PCD grinding process and thus enables a more efficient process design.