Climate-driven ocean warming is facilitating the expansion of thermophilic invasive species such as Pinctada radiata in the Mediterranean Sea. This study examined the species’ physiological responses to thermal gradients near the Delimara Power Station (Malta) to evaluate its potential as an early climate-change bioindicator. Specimens were collected from three sites along a temperature gradient (26.3 °C, 27.1 °C, 28.5 °C), and gill and adductor muscle tissues were analyzed for redox state biomarkers (ROS, oxidative damage to lipids—HPs and proteins—CO), antioxidant capacity (in vitro susceptibility to oxidants—∆HPs, total antioxidant capacity—TAC, glutathione peroxidase—GPx, and glutathione reductase—GR activity), and aerobic metabolism (cytochrome c oxidase, COX). Data were statistically analyzed by one-way ANOVA followed by Tukey’s post hoc test. Gill and muscle tissues responded differently to warming. The gills showed little change at 27.1 °C, but at 28.5 °C their antioxidant defenses declined, resulting in higher HP content and reduced antioxidant enzyme activity. Muscle showed a dual response. At 27.1 °C it was more resilient, with lower oxidative damage and ∆HPs and stronger antioxidant defense. At 28.5 °C it remained well adapted but exhibited higher ∆HPs and reduced TAC and GR activity with respect to the muscles of oysters collected at 27.1 °C, indicating a decline in antioxidant capacity. COX activity, which remains unchanged in the gills at both elevated temperatures, showed a significant reduction in the muscles of oysters collected from hottest waters, suggesting a shift toward anaerobic metabolism. Overall, P. radiata exhibited high thermal tolerance and physiological plasticity, supporting its persistence in heat-impacted environments. Although the presence of the invasive species P. radiata reflect climate-related ecological pressure, its physiological responses as a climate sentinel indicate that even near optimal temperatures its redox balance is altered, potentially threatening its survival as Mediterranean Sea temperatures continue to rise. These findings are relevant for predicting ecosystem changes under global warming.