In this study we compared some aspects of the physiology of the invasive blue mussel species Mytilus trossulus and the native Mytilus edulis in the White Sea. We registered the heart activity of M. edulis, M. trossulus and the hybrids in situ for two years and tested their thermal tolerance in a laboratory experiment. In situ monitoring showed that the heart rate, as well as its variability, was greater in the invasive species and the hybrids than in the native mussel species. At the same time, the native species showed a higher thermal tolerance in the laboratory experiment. Our results suggest that, when it comes to adaptation to increased temperature, M. edulis has a greater physiological potential than M. trossulus. In a warming climate, the invasive species may lose in competition with the native one due to a higher level of metabolism.