This paper presents the analysis of the dielectric characteristics of a hot $SF_6$ gas in a gas circuit breaker. Hot gas flow is analyzed using the FVFLIC method considering the moving boundary, material properties of real $SF_6$ gas, and arc plasma. In the arc model, the re-absorption of the emitted radiation is approximated with the boundary source layer where the re-absorbed radiation energy is input as an energy source term in the energy conservation equation. The breakdown criterion of a hot gas is predicted using the critical electric field as a function of temperature and pressure. To validate the simulation method, breakdown voltage for a 145kV 40kA circuit breaker was measured for various conditions. Consistent results between the simulation and experiment were confirmed.