Accurately forecasting the response of global biota to warming is a fundamental challenge for ecology in the Anthropocene. Within-species variation in thermal sensitivity, caused by phenotypic plasticity and local adaptation of thermal limits, is often overlooked in assessments of species responses to warming. Despite this, implicit assumptions of thermal niche conservatism or adaptation and plasticity at the species level permeate the literature with potentially important implications for predictions of warming impacts at the population level. Here we review how these attributes interact with the spatial and temporal context of ocean warming to influence the vulnerability of marine organisms. We identify a broad spectrum of thermal sensitivities among marine organisms, particularly in central and cool-edge populations of species distributions. These are characterized by generally low sensitivity in organisms with conserved thermal niches, to high sensitivity for organisms with locally adapted thermal niches. Important differences in thermal sensitivity among marine taxa suggest that warming could adversely affect benthic primary producers sooner than less vulnerable higher trophic groups. Embracing the spatial, temporal and biological context of within-species variation in thermal physiology helps explain observed impacts of ocean warming and can improve forecasts of climate change vulnerability in marine systems. This article is part of the theme issue 'Physiological diversity, biodiversity patterns and global climate change: testing key hypotheses involving temperature and oxygen'.