Climate envelope models (CEMs) have been used to predict the distribution of species under current, past, and future climatic conditions by inferring a species' environmental requirements from localities where it is currently known to occur. CEMs can be evaluated for their ability to predict current species distributions but it is unclear whether models that are successful in predicting current distributions are equally successful in predicting distributions under different climates (i.e. different regions or time periods). We evaluated the ability of CEMs to predict species distributions under different climates by comparing their predictions with those obtained with a mechanistic model (MM). In an MM the distribution of a species is modeled based on knowledge of a species' physiology. The potential distributions of 100 plant species were modeled with an MM for current conditions, a past climate reconstruction (21 000 years before present) and a future climate projection (double preindustrial CO2 conditions). Point localities extracted from the currently suitable area according to the MM were used to predict current, future, and past distributions with four CEMs covering a broad range of statistical approaches: Bioclim (percentile distributions), Domain (distance metric), GAM (general additive modeling), and Maxent (maximum entropy). Domain performed very poorly, strongly underestimating range sizes for past or future conditions. Maxent and GAM performed as well under current climates as under past and future climates. Bioclim slightly underestimated range sizes but the predicted ranges overlapped more with the ranges predicted with the MM than those predicted with GAM did. Ranges predicted with Maxent overlapped most with those produced with the MMs, but compared with the ranges predicted with GAM they were more variable and sometimes much too large. Our results suggest that some CEMs can indeed be used to predict species distributions under climate change, but individual modeling approaches should be validated for this purpose, and model choice could be made dependent on the purpose of a particular study.