The ability to predict the consequences of fluctuating environments on species distribution and extinction often relies on determining the tolerances of species or genotypes in different constant environments (i.e. determining tolerance curves). However, very little is known about the suitability of measurements made in constant environments to predict the level of adaptation to rapidly fluctuating environments. To explore this question, we used bacterial clones adapted to constant or fluctuating temperatures and found that measurements across a range of constant temperatures did not indicate any adaptation to fluctuating temperatures. However, adaptation to fluctuating temperatures was only apparent if growth was measured during thermal fluctuation. Thus, tolerance curves based on measurements in constant environments can be misleading in predicting the ability to tolerate fast environmental fluctuations. Such complications could lead to false estimates of the genetic merits of genotypes and extinction risks of species due to climate change-induced thermal fluctuations.