This paper presents the constrained thermodynamic optimization of a crossflow heat exchanger with ram air on the cold side. The ram-air stream passes through a diffuser before entering the heat exchanger, and exits through a nozzle. This configuration is used in the environmental control systems of aircraft. In the first part of the study the heat exchanger is optimized alone, subject to fixed total volume and volume fraction occupied by solid walls. Optimized geometric features such as the ratio of channel spacings and flow lengths are reported. It is found that the optimized features are relatively insensitive to changes in other physical parameters of the installation. In the second part of the study the entropy generation rate also accounts for the irreversibility due to discharging the ram-air stream into the atmosphere. The optimized geometric features are relatively insensitive to this additional effect, emphasizing the robustness of the thermodynamic optimum.