The thermal design of a counterflow heat exchanger using air as the working fluid was performed with two distinct goals: minimum inlet temperature difference and minimum number of entropy generation units. The heat exchanger was constituted by a double-finned conductive plate closed by adiabatic walls at the fin tips on both sides. The hot and cold air flows were considered in the turbulent regime, driven by a constant pressure head. The thermal load was constant, and an optimization was performed to obtain the optimum fin spacing and thickness, according to the two design criteria. A computer program was employed to evaluate the optimum conditions based on correlations from the literature. The results obtained from both design criteria were compared to each other. A scale analysis was performed considering the first design goal and the corresponding dimensionless parameters were compared with the results from the correlations.