Climate change caused by global warming involves crucial plant growth factors such as atmospheric CO2 concentration, ambient temperature or water availability. These stressors usually co‐occur, causing intricate alterations in plant physiology and development. This work focuses on how elevated atmospheric CO2 levels, together with the concomitant high temperature, would affect the physiology of a relevant crop, such as broccoli. Particular attention has been paid to those defence mechanisms that contribute to plant fitness under abiotic stress. Results show that both photosynthesis and leaf transpiration were reduced in plants grown under climate change environments compared to those grown under current climate conditions. Furthermore, an induction of carbohydrate catabolism pointed to a redistribution from primary to secondary metabolism. This result could be related to a reinforcement of cell walls, as well as to an increase in the pool of antioxidants in the leaves. Broccoli plants, a C3 crop, grown under an intermediate condition showed activation of those adaptive mechanisms, which would contribute to coping with abiotic stress, as confirmed by reduced levels of lipid peroxidation relative to current climate conditions. On the contrary, the most severe climate change scenario exceeded the adaptive capacity of broccoli plants, as shown by the inhibition of growth and reduced vigour of plants. In conclusion, only a moderate increase in atmospheric CO2 concentration and temperature would not have a negative impact on broccoli crop yields.