Data of the effects of the temperature on routine and low and high metabolic rate of Octopus maya are showed jointly with the antioxidant defence mechanisms of male and females of this octopus species. Raw data of adults exposed at 24, 26 and 30°C, and the raw data of the Catalase, superoxide dismutase, total glutathione, glutathione-s-transferace, lipoperoxidation, and protein carbonylation of octopus hearts and muscle. are showed.