We present the design and thermal characteristics of a levitating rotor in a superconducting magnetic bearing (SMB) system that is designed for a polarization modulator of a cosmic microwave background (CMB) polarization experiment. Thermal characteristics of the levitating rotor in the SMB are important to reduce the detector noise. We have constructed two types of SMB systems that both employ a NdFeB permanent magnet as a rotor and a YBCO superconductor array as a stator. One is the 1/6 scale prototype model and the other one is the flight representative full-scale prototype. In order to build a thermal model of the SMB system, we estimate thermal properties of a NdFeB magnet based on the measured data using the 1/6 scale prototype model. The thermal model is expanded to the full-scale prototype, and we obtained the requirement of heat loads from the SMB system is to be less than 1 mW. We also measured the thermal conductivity between the levitating rotor and a holder mechanism, which is the thermal path when the rotor is held in place at the time of field cooling. The measured conductivity is 1.34 mW/K, which is almost same as the 1/6 scale prototype model.