1. Transgenerational effects, non-evolutionary processes by which environmental conditions in one generation influence the performance in subsequent generations, are hypothesised to have substantial consequences for population dynamics under stochastic environments. However, any direct apparent detriment or advantage these processes generate for a focal species may be counteracted by concurrent effects upon interacting species. 2. Using an experimental Drosophila-parasitoid model system, we determined how the previous generation's thermal environment impacts the thermal performance of both hosts and parasitoids. We found substantial responses in both trophic-levels, with potential evidence for both condition-transfer effects and adaptive transgenerational plasticity. 3. We used these results to parameterise discrete-time simulation models to explore how transgenerational effects of thermal conditions and temporal autocorrelation in temperature are expected to impact the time to extinction for this host-parasitoid system under climate change. The models predicted that transgenerational effects would significantly hasten the time to extinction, largely through a reduction in estimated average performance. Under the assumptions of one of the population dynamics models trialled, we identified an additional hastening of extinction from the combined effect of both host and parasitoid transgenerational effects. 4. Our research demonstrates how community-level consequences of transgenerational effects may impact a population's sensitivity to climate change under a fluctuating environment and highlights the need to quantify and contextualise thermal transgenerational effects in their ecological setting.