Understanding how natural populations will respond to rapid anthropogenic climate change is one of the greatest challenges for ecologists and evolutionary biologists. Much research has focussed on whether physiological traits can evolve quickly enough under rapidly increasing temperatures. While the simple Breeder's equation helps to understand how extreme temperatures and genetic variation might drive within-population evolution under climate change, it does not consider two key areas: how different forms of phenotypic plasticity interact and variation among populations. Plasticity can modify the exposure to climatic extremes and the strength of selection from those extremes, while differences among populations provide adaptive diversity not apparent within them. Here, we focus on terrestrial vertebrates and, with a case study on a tropical lizard, demonstrate the complex interplay between spatial, genetic and plastic contributions to variation in climate-relevant physiological traits. We identify several problems that need to be better understood: which traits are under selection in a changing climate; the different forms of plasticity relevant to population persistence and rapid evolution; plastic versus genetic contributions to geographic variation in climate-associated traits and whether plasticity can be harnessed to promote persistence of species. Given ongoing uncertainties around whether natural populations can evolve rapidly enough to persist, we advocate the use of field trials aimed at increasing rates of adaptation, especially in systems known to be strongly impacted by human-driven changes in climate.