Abstract
How well populations can cope with global warming will often depend on the evolutionary potential and plasticity of their temperature‐sensitive, fitness‐relevant traits. In Bechstein's bats ( Myotis bechsteinii ), body size has increased over the last decades in response to warmer summers. If this trend continues it may threaten populations as larger females exhibit higher mortality. To assess the evolutionary potential of body size, we applied a Bayesian ‘animal model’ to estimate additive genetic variance, heritability and evolvability of body size, based on a 25‐year pedigree of 332 wild females. Both heritability and additive genetic variance were reduced in hot summers compared to average and cold summers, while evolvability of body size was generally low. This suggests that the observed increase in body size was mostly driven by phenotypic plasticity. Thus, if warm summers continue to become more frequent, body size likely increases further and the resulting fitness loss could threaten populations.