A bet-hedging strategy sacrifices fitness in average environments in exchange for increased fitness in rare but calamitous environments. It is unclear how such strategies can persist when selection is expected to improve suboptimal traits in the short-term. Bet hedging can persist if the ability to adaptively track environments is constrained in the short-term. To test this hypothesis, we evolve bet hedging under fluctuating selection of heat shocks using Saccharomyces cerevisiae and ask whether it has evolved as a constraint on adaptive tracking. We select for the retention of the bet-hedging trait through continual reduction in the frequency of heat shocks across two evolution regimes, viz. Regime-A (high frequency heat shocks) and Regime-B (low frequency heat shocks). We observed the retention of heat shock tolerance in lines from Regime-B but not Regime-A, suggesting the evolution of a constraint on adaptive tracking in lines from Regime-B relative to lines from Regime-A.