Propulsion systems in future hypersonic vehicles will require use of actively cooled structures that can withstand extreme thermomechanical loads. Candidate designs and materials for such structures have previously been identified through conventional yield-based design principles. The present article out- lines an approach that utilizes concepts of localized plasticity and shakedown under cyclic loading in the design process. For this purpose, an established computational technique is used to determine shakedown limits for prototypical cooled structures. The results are employed in a design sensitivity study. The study demonstrates that, by allowing for shakedown, structures with areal densities significantly lower than those obtained from yield-limited design can be obtained. The magnitude of the benefits depends on the specific geometry of interest, the thermomechanical boundary conditions and the constraints placed on the design.