Climate 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, while its established congener Mytilicola intestinalis has had >90 years to adapt. In laboratory experiments with temperatures 10°C-26°C, representing current and future temperatures, the development of both life cycle stages of both species accelerated with increasing temperature. In the free living infective stages of both species the development speed increase was largest between the two lowest temperatures (10°C and 14°C), with the small increases across the higher temperatures (18°C-26°C) being larger for the recent invader. In the parasitic stages, the growth of the established invader increased evenly from 10°C to 22°C, while the recent invader barely grew at 10°C gaining its maximum growth speed 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. Based on long-term temperature data and predictions, the numbers of completed life cycles per year will increase for both parasites. Overall, our experiments indicate that the main effect of temperature on both species is through development speed and not life cycle stage transition success. While the established invader seems better adapted for low current temperatures (around 10°C), 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.