This article deals with the time histories of the air flow rate required and the temperature of chilled air produced during cooling of air by melting ice with specified heat flux at the free liquid surface. The equations for estimating the required mass flow rate of air to maintain a specified heat flux removal of cool thermal discharge by direct contact of air with melting ice to produce chilled air were derived from an analysis of the heat transfer coupled with the moving boundary. Numerical examples are illustrated in which the inlet air temperatures were either specified or varied with time to simulate practical systems.