The green shore crab (Carcinus maenas) is native to Western Europe but has spread around the globe and is described as one of the top 100 worst invasive species. On the east coast of North America, their northern-most limit is the island of Newfoundland, Canada, where they can experience water temperatures as low as −1 °C. We investigated the physiological responses of C. maenas to a temperature reduction regime as well as to long-term acclimation to temperatures representative of winter (2 °C) and summer (12 °C) in Newfoundland. Heart rate, oxygen consumption and estimated energy expenditure declined steadily with decreasing temperature, but a marked change was observed between 6 and 4 °C, with lowest levels recorded in 2 °C. After long-term acclimation to 2 °C there was a sustained reduction in physiological parameters. Even though these physiological parameters were very low in 2 °C, the crabs still exhibited intermittent activity. This supports the presence of a dormancy, rather than true torpor/hibernation below 5 °C, in which crabs will continue to actively move and feed, albeit much more slowly. The population in Newfoundland contains haplotypes from both the invasive northern and southern lineages, and they appear to retain a similar low temperature response compared with most other populations of green crab from both their native and expanded range.