Cooling technologies, including refrigeration and air conditioning, pose significant challenges in terms of energy usage and environmental impact. Nearly 25% of electricity usage in the United States arises from cooling, and carbon-based emissions from cooling systems alone are expected to double by the end of 2050. Thermoelectric devices can be used to address both problems; however, a major bottleneck is low device efficiency due to the conflicting nature of material properties that must be optimized to achieve effective power conversion. As a result, large-scale searches for new high-efficiency thermoelectric materials are necessary. Here, we show that topological insulators are a promising class of materials for next-generation thermoelectrics. Using a combination of density functional theory (high-performance computing) and k.p perturbation theory (pencil-and-paper), we find that the band inversion strength is a key property of topological insulators that influences the thermoelectric performance. We evaluate the band inversion strengths of a large set of topological insulators, resulting in the prediction that NaCaBi is a particularly promising thermoelectric candidate. Perhaps more importantly, the high-throughput workflow used in this study establishes a blueprint for discovering yet-to-be-realized materials, paving the way for a new era of thermoelectrics-based cooling technologies.