Sex in many organisms is a dichotomous phenotype--individuals are either male or female. The molecular pathways underlying sex determination are governed by the genetic contribution of parents to the zygote, the environment in which the zygote develops or interaction of the two, depending on the species. Systems in which multiple interacting influences or a continuously varying influence (such as temperature) determines a dichotomous outcome have at least one threshold. We show that when sex is viewed as a threshold trait, evolution in that threshold can permit novel transitions between genotypic and temperature-dependent sex determination (TSD) and remarkably, between male (XX/XY) and female (ZZ/ZW) heterogamety. Transitions are possible without substantive genotypic innovation of novel sex-determining mutations or transpositions, so that the master sex gene and sex chromosome pair can be retained in ZW-XY transitions. We also show that evolution in the threshold can explain all observed patterns in vertebrate TSD, when coupled with evolution in embryonic survivorship limits.