A model of ice melting has been developed to produce chilled air during on-peak power consumption. Equations have been derived for estimating the thickness of the melted ice and the temperature distribution in the liquid region with convection boundary condition. Three test cases have been studied in which the air temperature was specified and varied with time. Results are given for the thickness of the melted ice layers for cool thermal discharges. The cool thermal discharge and the penetration distance for ice melting, increase with air velocity, especially at low velocities of about 10 m/s; they decrease weakly as the length traversed by air increases.