Μeagre (Argyrosomus regius) is a newly introduced species in the aquaculture sector characterized by high growth rates and good nutritional value. However, the optimum conditions such as water temperature for the rearing of this species are still under research. The aim of the present study was to investigate several biochemical responses in the heart, muscle, liver, and intestine of meagre reared under different water temperatures (17, 23, and 26 °C) in comparison to the initial acclimation temperature at 20 °C. To assess its cellular stress response, the molecular markers of Hsp70 and Hsp90 induced levels, p38 MAPK and p44/42 MAPK phosphorylated levels, ubiquitin conjugates, and Bcl-2 levels were determined. Moreover, to investigate its antioxidant defense, the activities of superoxide dismutase, catalase, and glutathione reductase were measured. The obtained results in meagre showed a distinct tissue-specific response regarding the variations observed in the studied parameters under different acclimation temperatures. Specifically, most examined tissues presented a decrease in the levels of the examined markers compared to 20 °C, while in the intestine, an increase of Hsp70 and p38 MAPK levels was observed at 23 and 26 °C. However, data on the final weight and length of the fish lead to the conclusion that high water temperatures such as 26 °C might be the best for the rearing of this species. Therefore, it is assumed that the observed differential molecular responses may act in a cell-protective way at all temperatures, irrespectively of the effect of temperature on growth parameters.