In this paper, we investigate a slow rarefied gas flow past a circular disk with an emphasis on the thermal polarization effect. First, the behavior of the gas is numerically studied based on the Bhatnagar–Gross–Krook model of the Boltzmann equation and the diffuse reflection boundary condition, under the assumption that the system can be linearized. A key highlight of the numerical results is the localization of temperature variations near the edge of the disk in the near-continuum regime. Consistent with previous studies, we find that the temperature near the edge displays distinct behavior, differing from the classical kinetic boundary layer typically observed near smooth boundaries. Next, we explore the role of the free motion of gas molecules and construct a simplified toy model to interpret the above numerical results. The model demonstrates qualitative agreement with the numerical results, providing valuable insights into the observed phenomena.