A thermal-hydraulic design study of the proposed ESPRESSO blanket for the Tandem Mirror Fusion Reactor is presented. Two solid breeder/multiplier configurations have been selected for the study: one with natural Li2O as solid breeder and no neutron multiplier and the other with 30% enriched gamma-LiAlO2 as solid breeder and Be as multiplier. A systematic procedure has been developed which effectively reduces the number of independent parameters to two, namely the neutron first wall loading and the main flow bulk temperature rise. Their effect on the maximum multiplier and breeder temperatures and on the pumping power ratio is investigated. Maximum allowable breeder and multiplier temperature constraints limit the design choice and a design point has been obtained for each case for a given maximum allowable pumping power ratio.