Sex determination is often seen as a dichotomous process: individual sex is assumed to be determined either by genetic (genotypic sex determination, GSD) or by environmental factors (environmental sex determination, ESD), most often temperature (temperature sex determination, TSD). We endorse an alternative view, which sees GSD and TSD as the ends of a continuum. Both effects interact a priori, because temperature can affect gene expression at any step along the sex-determination cascade. We propose to define sex-determination systems at the population- (rather than individual) level, via the proportion of variance in phenotypic sex stemming from genetic versus environmental factors, and we formalize this concept in a quantitative-genetics framework. Sex is seen as a threshold trait underlain by a liability factor, and reaction norms allow modeling interactions between genotypic and temperature effects (seen as the necessary consequences of thermodynamic constraints on the underlying physiological processes). As this formalization shows, temperature changes (due to e.g., climatic changes or range expansions) are expected to provoke turnovers in sex-determination mechanisms, by inducing large-scale sex reversal and thereby sex-ratio selection for alternative sex-determining genes. The frequency of turnovers and prevalence of homomorphic sex chromosomes in cold-blooded vertebrates might thus directly relate to the temperature dependence in sex-determination mechanisms.