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We investigated the impact of sublethal thermal stress on physiological rates of the copepod Paracartia grani , and explored the influence of previous thermal history on this response. The copepods, originally reared at 19 °C, were raised for 23 generations at 22 °C and 25 °C, and posteriorly exposed for 7-d to stress temperature (28 °C). The copepod acclimation capacity was assessed by comparing metabolic balance at 28 °C against their respective rearing temperatures. There was an inverse relationship between rearing temperature and body size and carbon content for the reared copepod lines. Weight-specific rates, except respiration, increased with rearing temperature, whereas per capita rate differences were levelled, partly due to differences in copepod size. Heat stress impact, as weight-specific rate fold-change, appeared inversely related to rearing temperature. Carbon gains were overall sufficient and slightly in excess to account for carbon losses. Gross-growth efficiency across warming scenarios was conserved, emphasizing resilience to environmental change. Our findings underscore the importance of considering the species' thermal history when predicting the response of copepod populations to climate change associated phenomena such as gradual slow ocean warming or heatwave events. • Copepods under multigenerational warming show alike physiological performance. • Vital rates of warm-reared copepods are less impacted by sublethal acute heat stress. • Copepods can maintain their metabolic balance under different thermal scenarios. • Reproductive effort is maintained under chronic warming and heat stress. [ABSTRACT FROM AUTHOR]