REBCO coated conductors are widely used for HTS power application, high magnetic field magnet application, and etc. A thermal stability of the REBCO conductor is essential for the operation of HTS-based device, and thermal conductivities of the conductor are relevant parameters for modeling cryogenic heat transfer. REBCO conductors consist of a REBCO layer, copper layers for electrical stabilization and a hastelloy substrate. At cryogenic temperature, thermal conductivity of copper and silver strongly depend on the purity of the material and the intensity of the magnetic field. In this study, thermal conductivities of the laminated composite structure of REBCO conductor are evaluated by using the thermal network model and the multidimensional heat conduction analysis. As a result, the thermal network model is applicable to REBCO conductors configured in series or parallel alone and multidimensional heat conduction analysis is necessary for complex cases of series and parallel configuration.