Abstract The effect of the thermal environment on performance and productivity has been a focus of interest among indoor environmental researchers for nearly a century, but most of that work has been conducted in relative isolation from the cognate disciplines of human performance evaluation. The present review examines thermal environmental effects on cognitive performance research conducted across multiple disciplines. After differentiating performance from productivity, we compare the two dominant conceptual models linking thermal stress to performance; (1) the inverted-U concept and (2) the extended-U relationship. The inverted-U specifies a single optimum temperature (or its corresponding subjective thermal sensation) at which performance is maximised. In contrast, the extended-U model posits a broad central plateau across which there is no discernible thermal effect on cognitive performance. This performance plateau is bounded by regions of progressive performance decrements in more extreme thermal conditions. The contradictions between these opposing conceptual models might derive from various confounding factors at play in their underlying research bases. These include, inter alia, environment-related, task-related, and performer-related factors, as well as their associated two-way and three-way interaction effects. Methodological discrepancies that might also contribute to the divergence of these conceptual models are evaluated, along with the proposed causal mechanisms underlying the two models. The weight of research evidence reviewed in this paper suggests that the extended-U hypothesis fits the relationship between moderate thermal environments and cognitive performance. In contrast to the inverted-U relationship, implemention of the extended-U in indoor climate control implies substantial reductions in building energy demand, since it permits the heating and cooling setpoint deadband to expand across the full width of the thermal comfort zone, or even slightly further during emergencies such as peak demand events on the electricity grid. Use of personal comfort systems can further extend the thermostat setpoint range beyond the comfort zone.