Most organisms face variable environmental conditions. Strategies to cope with such variation are e.g., bet-hedging, dispersal, or tolerance. With a systematic trend in temperature or other environmental characteristics, e.g., under climate change, species also experience selection pressure towards a changing environmental optimum. Here, we simulate the evolution of niche optimum and width (tolerance) in isolated populations, under different scenarios: (1) environmental conditions are static (constant mean and standard deviation; control) or follow a trend in (2) the mean, (3) the variance, or (4) in both, simulating the predicted effects of climate change. Tolerance trades off against maximum fertility (fitness). Results show that populations can evolutionarily track a trend in mean conditions as long as change does not proceed too fast. An increase in variance, however, can be more detrimental, due to the inherent trade-offs associated with enlarging tolerance. Indeed, for any given trade-off, a theoretical upper boundary exists for the evolution of tolerance: if environmental variance becomes too large, populations cannot evolve sufficient tolerance and go extinct. An increasing variance can never be tracked indefinitely if a trade-off as assumed here exists. Importantly, climate change models often focus on the impact of increasing mean temperatures only. Here, we show that including the projected increase in environmental variance may change results considerably.