This paper establishes a multidisciplinary method combining conjugate heat transfer (CHT) and thermal stress for a high-temperature Ni-based superalloy turbine rotor blade with integrated cooling structures. A conjugate calculation is performed to investigate the coolant flow characteristics, heat transfer, and thermal stress of the rotor blade under rotating and stationary conditions to understand the effects of rotation on the multidisciplinary design of the blade. Furthermore, the maximum resolved shear stress among the 30-slip systems and the corresponding dominant slip system are obtained to predict the deformation tendency of the blade by employing the crystal plasticity finite element method (CPFEM) and considering the specified anisotropic blade material (GTD-111). The results show that the forces of rotation, including centrifugal and Coriolis forces, and their induced buoyancy force, alter the coolant flow field and thus affect the rotor blade’s heat transfer distribution compared with the stationary condition. The maximum temperature and thermal stress of the rotor blade under rotating conditions are reduced by 5% and 21% compared with that under the stationary condition, respectively. Compared with the stationary condition, the temperature and thermal stress distribution on the blade under the rotating condition are more uniform, especially on the suction side. In addition, the blade root connecting with the hub, the film holes near the leading-edge region at the blade root, the mid-chord of the suction surface, and the grooved blade tip are easily damaged by the enormous resolved shear stress and the interface effect of different types of dominant slip system under the two conditions. In this work, it was feasible to use the cascade cooling effect test to analyze the dynamic test results for the rotor blade. Furthermore, the thermal stress analysis based on the CPFEM can provide a superior level of blade cooling design than CHT by considering the anisotropic material characteristics of a turbine blade.