Invasive species with native ranges spanning strong environmental gradients that establish in new habitats are particularly well-suited for examining the roles of selection and population history in rapid environmental adaptation, providing insight into potential evolutionary responses to climate change. The Atlantic oyster drill (Urosalpinx cinerea) is a marine snail with a native range spanning the strongest marine thermal gradient in the world that has established invasive populations on the U.S. Pacific coast. Here, we leverage this system using genome-wide SNPs and environmental data to examine invasion history and identify genotype-environment associations indicative of local adaptation across its native range, and then assess evidence for predicted allelic frequency shifts signaling rapid adaptation in invasive populations. We demonstrate strong genetic structuring among native regions aligned with life history expectations and identify southern New England as the source of invasive populations. We also identify putatively thermally adaptive loci across the native range, for which two invasive populations show significant divergence from source populations. However, we find no evidence of directional shifts in allele frequencies as would be predicted by environmental selection, suggesting that divergence is likely due to genetic drift rather than rapid adaptation. Alternatively, the success of new populations in environments differing from their origin may be due to relaxed selection pressures associated with more benign conditions, and/or standing capacity for phenotypic plasticity. This demonstrates the utility of invasive species for understanding evolutionary responses to changing environments, and the importance of considering population history and environmental selection pressures when evaluating adaptative capacity.