<p>The study of Surface Air Cooled Oil Coolers (SACOC) is motivated by the need for new cooling concepts for compact machinery designs with high thermal load. Installing finned heat exchangers in the bypass duct of a turbofan engine provides an additional cooling source having transonic flow as a heat sink. The characterization of the heat transfer and the aerodynamics of the design are essential to minimize the impact on the overall efficiency of the engine. In the present study, the SACOC is studied numerically and experimentally. Two geometries are tested in a high-speed linear wind tunnel where measurements are taken with multiple sensors and optical techniques. For the heat transfer characterization, an Inverse Heat Conduction Methodology (IHCM) based on a Levenberg-Marquardt Algorithm is developed. The experimental results are matched to numerical simulations using a Reynolds Averaged Navier-Stokes (RANS) solver. Finally, a multi-objective optimization algorithm is coupled <a>with the RANS solver</a> to explore new geometries that maximize the heat transfer and minimize the pressure drop across the studied domain. The 400 profiles generated allow for the identification of the features that have a higher influence on the performance of the fins and six profiles that present large improvements are chosen for further analysis.</p>