The authors incorporate mechanistic information about lizard physiological responses to heat into predictions of trait variation across time and space, finding that the range of functional traits is more constrained in locations where the local climate strongly selects for thermal performance. A major challenge in ecology and evolution is to disentangle the mechanisms driving broad-scale variation in biological traits such as body size, colour, thermal physiology traits and behaviour. Climate has long been thought to drive trait evolution and abiotic filtering of trait variation in ectotherms because their thermal performance and fitness are closely related to environmental conditions. However, previous studies investigating climatic variables associated with trait variation have lacked a mechanistic description of the underpinning processes. Here, we use a mechanistic model to predict how climate affects thermal performance of ectotherms and thereby the direction and strength of the effect of selection on different functional traits. We show that climate drives macro-evolutionary patterns in body size, cold tolerance and preferred body temperatures among lizards, and that trait variation is more constrained in regions where selection is predicted to be stronger. These findings provide a mechanistic explanation for observations on how climate drives trait variation in ectotherms through its effect on thermal performance. By connecting physical, physiological and macro-evolutionary principles, the model and results provide an integrative, mechanistic framework for predicting organismal responses to present climates and climate change.