The behavior of cool thermal discharges with direct in situ contact in crystal-melting operations to produce chilled air during off-peak power-consumption hours has been investigated. Equations have been derived for estimating the thickness of the melted ice and the temperature distribution in the liquid region with specified heat fluxes on the boundary. Three examples with different fluxes of cool thermal discharges are discussed. Limitations on the thicknesses of the melted ice layers for cool thermal discharges are delineated.