[en] Highlights: •Reducing filling gas pressure helps to improve capsule temperature uniformity. •Pure He is conducive for high temperature uniformity at stable cooling condition. •Cooling temperature fluctuation deteriorates the capsule temperature uniformity. •Amplitude of cooling temperature is attenuated to less than 10% by filling gas. •High H₂ gas yields better attenuation for cooling temperature fluctuation. -- Abstract: This paper presents a numerical study on the thermal distribution and cooling performance of indirect-drive inertial confinement fusion (ICF) cryogenic target which requires a highly uniform temperature distribution around its capsule. Computational Fluid Dynamics, CFD models are developed for both stable and transient fluctuating cooling conditions. Experimental validation is undertaken and the predicted amplitudes by CFD simulation prove to be in good agreement with those measured in the experiments. The investigation results indicate that the He-H₂ gas filled in the hohlraum has quite an impact on the thermal environment around capsule, and improvements in the uniformity of capsule surface temperature can be made by either reduction of filling gas pressure or increase of He content in gas mixture. Fluctuation of cooling temperature deteriorates the uniformity of capsule surface temperature when compared with stable cooling conditions. However, the fluctuation amplitude can be attenuated to less than 10% in the presence of filling gas, and increasing the content of H₂ in filling gas gives rise to further attenuation.