Ecological responses to global warming are likely driven by a combination of gradual warming trends and extreme climate events, which are increasing in frequency and intensity. Specifically, heatwaves may amplify the impact of ongoing warming, and thus affect species’ physiological responses, behaviour and eventually survival. Here, we tested the hypothesis that a tropical invasive grazer snail, Cerithium scabridum, will be more resilient to the effects of future gradual warming and marine heatwaves (MHWs) than its native congener C. lividulum, co-occurring in rocky intertidal pools along the Levantine coast. Survival and faecal production (as a proxy for feeding rate) of the 2 species were measured under 4 experimental temperature conditions: ambient summer mean (31°C), predicted warming scenario (ambient +3°C), and short-term MHWs (+5°C) added to either ambient or warming treatments, followed by a recovery period. No effect of warming alone was detected on either species, whereas MHW reduced faecal production only in the native C. lividulum. During the recovery period, C. lividulum survival dropped, but the few surviving individuals recovered from the heat stress as indicated by the increase in faecal production. Neither snail species survived under the combination of warming and MHW. These results suggest that both species, living in a thermally fluctuating and often extreme environment, can tolerate a +3°C gradual warming, but only the invasive snail can withstand a +5°C heatwave. However, neither species can endure a severe heatwave on top of predicted gradual warming, potentially leading to population collapse among both species in the region.