A mathematical model for a desuperheater, transferring thermal energy from the discharge of a refrigerant compressor to heat service water, is presented. The model accounts for the geometry of a sample unit consisting of counterflow through concentric cylinders with a doubly augmented inner tube. Losses to the ambient (from the external water flow) and the effects of the venting ports in the inner tube are shown to be small. The analysis employs conventional heat transfer coefficient correlations and the NTU method.