Heat transfer at the nanoscale is an acoustic problem. In nonmetallic solids, heat is primarily carried by lattice vibrations (phonons), and its transfer can similarly be impeded by methods for manipulating vibrations familiar to acousticians. Metamaterials have seen increasing use in altering and controlling vibration. Metamaterial concepts, including periodic structuring of materials and introduction of resonant inclusions, have been used to control vibration on the macroscale, and can also affect heat transfer when implemented at nanoscale. Locally resonant materials appear to be able to address the frequency range responsible for heat transfer most easily. Control of heat transfer is of particular importance because heating and cooling buildings are among the most extensive human uses of energy, thus presenting a significant opportunity for societal benefit through increased efficiency. Even modest improvements in building insulation will result in significant energy and cost savings. In pursuit of a superior and cost-effective insulating material for building applications, an optimization of the nanostructure of a polymer metamaterial panel to reduce heat transfer is carried out using simulation in COMSOL and a genetic algorithm. Results of this research are presented here. [Funded by USDOE Office of Energy Efficiency and Renewable Energy (EERE)—Office of Building Technologies.]