Our study addresses the role of non-genetic and genetic inheritance in shaping the adaptive potential of populations under a warming ocean scenario. We used a combined experimental approach [transgenerational plasticity (TGP) and quantitative genetics] to partition the relative contribution of maternal vs. paternal (additive genetic) effects to offspring body size (a key component of fitness), and investigated a potential physiological mechanism (mitochondrial respiration capacities) underlying whole-organism growth/size responses. In very early stages of growth (up to 30 days), offspring body size of marine sticklebacks benefited from maternal TGP: offspring of mothers acclimated to 17 °C were larger when reared at 17 °C, and offspring of mothers acclimated to 21 °C were larger when reared at 21 °C. The benefits of maternal TGP on body size were stronger and persisted longer (up to 60 days) for offspring reared in the warmer (21 °C) environment, suggesting that maternal effects will be highly relevant for climate change scenarios in this system. Mitochondrial respiration capacities measured on mature offspring (F1 adults) matched the pattern of TGP for juvenile body size, providing an intuitive mechanistic basis for the maternal acclimation persisting into adulthood. Size differences between temperatures seen at early growth stages remained in the F1 adults, linking offspring body size to maternal inheritance of mitochondria. Lower maternal variance components in the warmer environment were mostly driven by mothers acclimated to ambient (colder) conditions, further supporting our tenet that maternal effects were stronger at elevated temperature. Importantly, all parent-offspring temperature combination groups showed genotype × environment (G × E) interactions, suggesting that reaction norms have the potential to evolve. To summarize, TGP and G × E interactions work in concert to mediate impacts of ocean warming on metabolic capacity and early growth of marine sticklebacks. TGP can buffer short-term detrimental effects of climate warming and may buy time for genetic adaptation to catch up, therefore markedly contributing to the evolutionary potential and persistence of populations under climate change.