The plane strain formulation of the thermal stress problem was used to obtain the thermal stresses in a rapidly cooled prismatic body for various aspect ratios and external conditions. The maximum principal stress in a body exposed to a constant ambient temperature during rapid cooling increased with Biot number. However, the thermal stress showed an extremum with change in aspect ratio. Controlling the ambient temperature to decrease exponentially can be used to decrease the maximum principal stress during cooling. General results are presented for various aspect ratios and cooling rates and may be applied to the design of process conditions for the cooling of sintered bodies, in particular, to avoid thermal fragmentation.