Rear (warm) edge populations are often considered more susceptible to warming than central (cool) populations because of the warmer ambient temperatures they experience, but this overlooks the potential for local variation in thermal tolerances. Here we provide conceptual models illustrating how sensitivity to warming is affected throughout a species' geographical range for locally adapted and non-adapted populations. We test these models for a range-contracting seaweed using observations from a marine heatwave and a 12-month experiment, translocating seaweeds among central, present and historic range edge locations. Growth, reproductive development and survivorship display different temperature thresholds among central and rear-edge populations, but share a 2.5 °C anomaly threshold. Range contraction, therefore, reflects variation in local anomalies rather than differences in absolute temperatures. This demonstrates that warming sensitivity can be similar throughout a species geographical range and highlights the importance of incorporating local adaptation and acclimatization into climate change vulnerability assessments.