Plants that can adapt their phenotype may be more likely to survive changing environmental conditions. Heritable epigenetic variation could provide a way to rapidly adapt to such changes. Here we tested whether environmental stress induces heritable, potentially adaptive phenotypic changes independent of genetic variation over few generations in Arabidopsis thaliana. We grew two accessions (Col-0, Sha-0) of A. thaliana for three generations under salt, heat and control conditions and tested for induced heritable phenotypic changes in the fourth generation (G4) and in reciprocal F1 hybrids generated in generation three. Using these crosses we further tested whether phenotypic changes were maternally or paternally transmitted. In generation five (G5), we assessed whether phenotypic effects persisted over two generations in the absence of stress. We found that exposure to heat stress in previous generations accelerated flowering under G4 control conditions in Sha-0, but heritable effects disappeared in G5 after two generations without stress exposure. Previous exposure to salt stress increased salt tolerance in one of two reciprocal F1 hybrids. Transgenerational effects were maternally and paternally inherited. Lacking genetic variability, maternal and paternal inheritance and reversibility of transgenerational effects together indicate that stress can induce heritable, potentially adaptive phenotypic changes, probably through epigenetic mechanisms. These effects were strongly dependent on plant genotype and may not be a general response to stress in A. thaliana.