AbstractClimate change may exacerbate the impact of invasive parasites from warmer climates through pre‐existing temperature adaptations. We investigated temperature impacts on two closely related marine parasitic copepod species that share the blue mussel (Mytilus edulis) as host: Mytilicola orientalis has invaded the system from a warmer climate <20 years ago, whereas its established congener Mytilicola intestinalis has had >90 years to adapt. In laboratory experiments with temperatures 10–26°C, covering current and future temperatures as well as heat waves, the development of both life cycle stages of both species accelerated with increasing temperature. In the parasitic stages, the growth of the established invader increased evenly from 10°C to 22°C, whereas the recent invader barely grew at all at 10°C and grew faster already at 18°C. In contrast, temperature had little effect on the transition success between life cycle stages. However, the highest temperature (26°C) limited the egg development success of the established invader and the host entry success of both species, whereas the infection success of the established invader increased at 18°C and 22°C. In general, our experiments indicate that the main effect of temperature on both species is through development speed and not life cycle stage transition success. Based on regional long‐term temperature data and predictions, the numbers of completed life cycles per year will increase for both parasites. The established invader seems better adapted for low current temperatures (around 10°C), whereas the more recent invader barely develops at these temperatures but can cope in high temperatures (around 26°C). Hence, pre‐existing temperature adaptations of the recent invader may allow the species to better cope with heat waves.