Climate change increases the frequency and severity of heatwaves that negatively affect plant survival and productivity. To investigate the possibility that heat stress primes plants and their offspring for future exposure, we exposed successive generations of Arabidopsis thaliana to severe heatwave conditions. Heat-primed offspring had a higher seed production after exposure to heat stress. DNA methylation mutants were more sensitive and showed no priming effect, whereas demethylation mutants showed the opposite response, confirming the involvement of DNA methylation in the response to the treatments. Consistently, bisulfite sequencing showed a global hypermethylation of genomic, conversely mitochondrial DNA revealed hypomethylation in response to heat. mRNA sequencing indicated that priming particularly affected genes related to the mitochondrial energy system and oxidative stress responses. Consistently, under heat conditions respiration rates and antioxidant enzymes activities (APX, POX, CAT, DHAR and MDHAR) were less increased, whereas soluble sugar and tocopherol levels were higher in primed plants. Under heat conditions membrane peroxidation (MDA) and protein carbonylation levels of primed plants were significantly lower, correlating with a lower increase of electrolyte leakage. These results demonstrate that heat stress induces heritable epigenetic changes involving DNA methylation affecting respiration and antioxidant activities enhancing the protection from oxidative damage. This increases the resilience of the plant and its progeny and affects our predictions of climate change responses of plants.