The thermal contact resistance (TCR) is one of the important resistance components in cryogenic systems. Cryogenic measurement devices using a cryocooler can be affected by TCR because the device has to consist of several metal components that are in contact with each other for heat transfer to the specimen without a cryogen. Therefore, accurate measurement and understanding of TCR is necessary for the design of cryogenic measurement devices using a cryocooler. The TCR occurs at the interface between metals and it can be affected by variable factors, such as the roughness of the metal surface, the contact area and the contact pressure. In this study, we designed a TCR measurement system at variable temperature using a cryocooler as a heat sink. Copper was selected as a specimen in the experiment because it is widely used as a heat transfer medium in cryogenic measurement devices. We measured the TCR between Cu and Cu for various temperatures and contact pressures. The effect of the interfacial materials on the TCR was also investigated.