A numerical model to obtain the temperature distribution in a radiation shield of cryogenic systems was proposed. Conformal mapping was used to transform the eccentric physical region of the upper plate to the concentric numerical region. The effects of the thickness of the radiation shield, the emissivities of the vacuum chamber and the radiation shield, and the eccentricity between the centers of the upper plate and the contact area with a cryocooler on the maximum temperature difference in a radiation shield were shown.