Human activity is causing climates to change more rapidly than at any time in the last 10,000 years. If populations of organisms are unable to effectively respond to changing environments, they will be at risk of extinction. In plants, two of the most important mechanisms of response to environmental change are phenotypic plasticity, where the same genotype expresses different phenotypes in different environments, and adaptation, which requires changes in allele frequency in populations as exposed individuals show variable survival and reproduction. Although most researchers accept the importance of both of these mechanisms, they are most commonly considered in isolation in models of response and persistence to climate change. Here, I use the model species Arabidopsis thaliana to investigate the interaction of plasticity and selection in fitness and phenology response to simulated climate warming, the effect of artificial selection on variation for plastic response and cross-generational effects of environmentally induced variation in flowering time. I also study the effects of varying rates of environmental fluctuation on evolvability on populations of self-replicating computer programs using the artificial life platform Avida. I find that a small increase in ambient temperature, in line with predictions for the next few decades, is able to elicit significant plastic responses and that these responses have the potential to alter population genetic structure and affect future evolution. I also find that selection on flowering time can reduce variation for plastic response and that non-genetic effects on flowering time can significantly alter germination in the next generation. Lastly, I find that rapidly changing environments in the long term can select for more evolvable populations and genotypes. These results highlight the importance of considering plasticity and evolution together if we are going to make accurate predictions of climate change response.