Temperature plays a vital role in shaping species' biology and biogeography, but the response of marine species to changes in temperature is still poorly understood over time scales relevant to climate change. In this thesis, I use a single species as a case study to explore acclimation and adaptation to temperature at the levels of gene sequence, gene expression, and whole-animal physiology. My study species is the European green crab, Carcinus maenas, a globally invasive temperate species that thrives across a wide range of environmental temperatures. By comparing an invasive species across seven populations in its native and invasive range, I was able to explore both short-term (invasive range) and long-term (native range) impacts of environmental temperature. To lay the groundwork for this project, I first review the literature on adaptation in marine invasive species. While quantitative research strongly suggests a role for adaptation, the dearth of integrated genetic-quantitative work severely limits our understanding of this process. The rest of this thesis attempts to fill this gap with empirical research. First, I describe the thermal physiology of green crabs in detail, and find that green crabs have high inherent eurythermality and acclimatory plasticity. Despite this thermal flexibility, I also observed potentially adaptive differentiation among populations, particularly within the native range. Population genetics supported a role for significant local adaptation between populations in the species' native range. I identified a number of specific genes likely involved in long-term adaptation between northern and southern native range populations, suggesting that innate immunity and muscle function may be under selection. These data also suggested a more limited role for ongoing, rapid adaptation in the species' invasive range. Patterns of gene expression integrate neatly with the genetic and physiological data, and I identified two groups of co-expressed genes whose expression appears related to adaptive differences in intraspecific physiology. Taken together, this project provides detailed, integrative evidence for the importance of acclimatory plasticity and both short- and long-term adaptation in success across a wide range of thermal environments in a high gene flow species. Finally, I discuss the broader implications of this work to species persistence in a rapidly changing ocean.