The effect of vacuum degradation in cryostat of a gamma spectrometer on the steady-state temperature of thermal shield and its efficiency are analyzed in this study. Considering the thermal load due to radiation, the thermal conductivity of residual gases and shield supports, the steady-state temperature of the shield is determined based on the differential energy balance equation for a simplified thermal model of the cryostat. A more complex model corresponding to the design of a real cryostat is simulated using computational fluid dynamics. The obtained temperature distribution is presented. The simulated results are compared with experimental data measured on an operating cryostat with a cryocooler in the temperature stabilization mode. The same measurements were carried out for a cryostat with and without a thermal shield, as well as with multilayer insulation. The obtained results confirm that the thermal shield provides decreasing heat transfer even for a vacuum degradation in a cryostat.