BackgroundOn-going global climate change poses a serious threat for natural populations unless they are able to evolutionarily adapt to changing environmental conditions (e.g. increasing average temperatures, occurrence of extreme weather events). A prerequisite for evolutionary change is within-population heritable genetic variation in traits subject to selection. In relation to climate change, mainly phenological traits as well as heat and desiccation resistance have been examined for such variation. Therefore, it is important to investigate adaptive potential under climate change conditions across a broader range of traits. This is especially true for life-history traits and defences against natural enemies (e.g. parasites) since they influence organisms’ fitness both directly and through species interactions. We examined the adaptive potential of fitness-related traits and their responses to heat waves in a population of a freshwater snail, Lymnaea stagnalis. We estimated family-level variation and covariation in life history (size, reproduction) and constitutive immune defence traits [haemocyte concentration, phenoloxidase (PO)-like activity, antibacterial activity of haemolymph] in snails experimentally exposed to typical (15 °C) and heat wave (25 °C) temperatures. We also assessed variation in the reaction norms of these traits between the treatments.ResultsWe found that at the heat wave temperature, snails were larger and reproduced more, while their immune defence was reduced. Snails showed high family-level variation in all examined traits within both temperature treatments. The only negative genetic correlation (between reproduction and antibacterial activity) appeared at the high temperature. However, we found no family-level variation in the responses of most examined traits to the experimental heat wave (i.e. largely parallel reaction norms between the treatments). Only the reduction of PO-like activity when exposed to the high temperature showed family-level variation, suggesting that the cost of heat waves may be lower for some families and could evolve under selection.ConclusionOur results suggest that there is genetic potential for adaptation within both thermal environments and that trait evolution may not be strongly affected by trade-offs between them. However, rare differences in thermal reaction norms across families indicate limited evolutionary potential in the responses of snails to changing temperatures during extreme weather events.Electronic supplementary materialThe online version of this article (doi:10.1186/s12862-017-0988-x) contains supplementary material, which is available to authorized users.