A cause-and-effect understanding of climate influences on ecosystems requires evaluation of thermal limits of member species and of their ability to cope with changing temperatures. Laboratory data available for marine fish and invertebrates from various climatic regions led to the hypothesis that, as a unifying principle, a mismatch between the demand for oxygen and the capacity of oxygen supply to tissues is the first mechanism to restrict whole-animal tolerance to thermal extremes. We show in the eelpout, Zoarces viviparus, a bioindicator fish species for environmental monitoring from North and Baltic Seas (Helcom), that thermally limited oxygen delivery closely matches environmental temperatures beyond which growth performance and abundance decrease. Decrements in aerobic performance in warming seas will thus be the first process to cause extinction or relocation to cooler waters.