Cryostats are usually designed in an empirical manner. Optimum design with respect to the helium evaporation, however, can only be realized by means of a computer. As a first step towards this Computer Aided Cryostat Design, the distributions of temperatures and heat flows in a pot-type cryostat with one or two vapour-cooled radiation shields are considered. In this paper attention is paid to the thermal analysis of these cryostats and some optimization results with respect to the actual design are presented. As an extension of the cryostat configuration the incorporation of a refrigerator is also considered.