Concentrated solar power (CSP) plants offer sustainable energy with the benefit of day-to-night energy storage. The recent development of the supercritical carbon dioxide (sCO2) Brayton cycle made CSP plants cost-competitive. However, the cost of cooling required for these CSP plants can vary wildly depending on design, and current cooler designs are far from optimal. Here, we optimize the design and configuration of a dry cooling system. We develop a physics-based simulation of the cooling properties of an air-cooled heat exchanger. Using this simulator, we leverage recent results in high-dimensional Bayesian optimization to find dry cooler designs that minimize lifetime cost, reducing this cost by about 67% compared to recently proposed designs. Our simulation and optimization framework can increase the development pace of economically viable sustainable energy generation systems.