The Charnov-Bull model stipulates that environmental sex determination (ESD) is favoured when fitness of the sexes responds differently to the environment. However, Charnov-Bull has not yet been broadly successful in explaining the adaptive significance of temperature-dependent sex determination (TSD), a form of ESD. Specifically, there is no broad and convincing explanation for the occurrence of a sex-by-incubation temperature interaction for fitness. Here, I point out that the Trivers-Willard model, which predates Charnov-Bull, has never been applied broadly to explain the adaptive significance of TSD. Under Trivers-Willard, a sex-by-environment interaction for fitness occurs along the axis of individual condition (general health, vigour, etc), as male fitness is relatively sensitive to condition by virtue of relatively strong sexual selection; this occurs regardless of the direction of sexual-size dimorphism. I propose that incubation temperature affects condition, and TSD evolves so that males arise from relatively high-quality incubation environments; I call this the Mighty Males hypothesis. Re-examination of existing literature provides significant support to Mighty Males and its assumptions. Mighty Males can also explain why aspects of the environment other than temperature affect sex in some TSD species. Ultimately, I provide a simple explanation for TSD, and I suggest directions for future work.