The stress physiology and welfare needs of red seabream, a fish species with high nutritional and economic value for aquaculture, have been poorly studied. The aim of the current study was to investigate physiological responses of red seabream to potential environmental and husbandry stress factors. We quantified the acute stress response of fish exposed to a standardized acute chasing stress protocol as well as to transportation stress, by analysing acute stress biomarkers such as plasma concentrations of cortisol, glucose, lactate and osmolality. Moreover, the physiological status of fish reared at different water temperatures (15, 20 and 25°C) was also studied by analysing plasma parameters and cortisol concentration in scales. Results showed that in most estimated parameters, red seabream showed a fast response and recovery to acute stress. On the contrary, recovery after an 18‐h transportation stress was prolonged and required more than one day. Finally, rearing of fish at different temperatures also affected stress indicators such as plasma cortisol and glucose, while lactate and osmolality were not significantly affected. Regarding cortisol concentration in fish scales, a chronic stress indicator, results showed that fish reared at 15°C had a significantly higher cortisol concertation of scales than those exposed to 25°C. The data provide a better insight into the effect of husbandry and environmental factors on red sea bream stress physiology and welfare.