Thermal conditioning of a gas during compression and expansion processes requires rapid transfer of heat. Proposed is a thin flexible membrane with a biologically-inspired, lung-like structure characterized by branching tubes, massive surface area, and low overall pressure drops. By forcing the working gas into contact with the large surface area of a thin membrane, rapid heat transfer may be achieved across the membrane and into a liquid bath. Inspiration and expiration of the gas is driven by volume changes in the liquid bath. A computational approach is taken to the design of the lung-like structure. First, Non-dominated Sorting Genetic Algorithm II (NSGA-II) is run to optimize elemental geometries for minimum pressure drop and maximum heat transfer. In the initial case, 2D elements are passed through Gambit and Fluent to evaluate the fitness function. Here, we present the results of the elemental optimization. In the future, 3D elements will be analyzed and connected in an optimal way to generate a 3D lung-like structure.