In plants, epigenetic stress memory has so far been found to be largely transient. Here, we wanted to assess the heritability of heat stress-induced epigenetic and transcriptomic changes following woodland strawberry (Fragaria vesca) reproduction. Strawberry is an ideal model to study epigenetic inheritance because it presents two modes of reproduction: sexual (self-pollinated plants) and asexual (clonally propagated plants named daughter plants). Taking advantage of this model, we investigated whether heat stress-induced DNA methylation changes can be transmitted via asexual reproduction. Our genome-wide study provides evidence for stress memory acquisition and maintenance in F. vesca. We found that specific DNA methylation marks or epimutations are stably transmitted over at least three asexual generations. Some of the epimutations were associated with transcriptional changes after heat stress. Our findings show that the strawberry methylome and transcriptome respond with a high level of flexibility to heat stress. Notably, independent plants acquired the same epimutations and those were inherited by their asexual progenies. Overall, the asexual progenies can retain some information in the genome of past stresses encountered by their progenitors. This molecular memory, also documented at the transcriptional level, might be involved in functional plasticity and stress adaptation. Finally, these findings may contribute to novel breeding approaches for climate-ready plants.