Marine heatwaves can have major and lasting effects on organism physiology and species persistence. Such temperature extremes are increasing in frequency, with consecutive heatwave events already occurring within the lifetime of many organisms. Heat stress memory (thermal priming) by individuals is a potential within-generation response to cope with recurring marine heatwaves. However, whether this form of biological memory can be inherited across generations is not well known. We used a three-generation experiment to investigate individual and transgenerational effects of single and recurring marine heatwaves on fitness-related traits using stickleback (Gasterosteus aculeatus) as a model species. We exposed adults (both sexes) to heatwaves, and assessed female reproductive output in both the parent and offspring generation, and offspring (both sexes) survival, growth, and behaviour to establish a holistic picture of potential heatwave effects on ectothermic fish. Exposure to single, extreme heatwaves lowered reproductive output, and decreased offspring exploratory behaviour, impeded capacity to respond to further thermal stress, and reduced long-term survival. However, prior experience of heatwaves (heat stress memory) mitigated some of these effects at both an individual (growth) and transgenerational (fecundity) level, indicating that species experiencing increasing heatwave frequency as part of ongoing climate change may cope better than previously thought.