Sex reversal at high temperatures during embryonic development (e.g. ZZ females) provides the opportunity for new genotypic crosses (e.g. ZZ male x ZZ female). This raises the alarming possibility that climatic warming could lead to the loss of an entire chromosome - one member of the sex chromosome pair (the Y or W) - and the transition of populations to environmental sex determination (ESD). Here we examine the evolutionary dynamics of sex-determining systems exposed to climatic warming using theoretical models. We found that the loss of sex chromosomes is not an inevitable consequence of sex reversal. A large frequency of ZZ sex reversal (50% reversal from male to female) typically divides the outcome between loss of the ZW genotype and the stable persistence of ZZ males, ZW females, and ZZ females. The amount of warming associated with sex chromosome loss depended on several features of wild populations - environmental fluctuation, immigration, heritable variation in temperature sensitivity, and differential fecundity of sex-reversed individuals. Chromosome loss was partially or completely buffered when sex-reversed individuals suffered a reproductive fitness cost, when immigration occurred, or when heritable variation for temperature sensitivity existed. Thus, under certain circumstances, sex chromosomes may persist cryptically in systems where the environment is the predominant influence on sex.