Mesoscale eddies are major regulators of air-sea heat exchange, yet their climatic impact has been assessed mainly through changes in eddy frequency or amplitude, implicitly assuming that the spatial organization of eddy-induced thermal anomalies is of secondary importance. Here, using 26 years of satellite observations, we show that global eddy-induced sea surface temperature anomalies (SSTAs) have shifted toward more coherent, monopole-like structures. This change corresponds to increases of approximately 4% per decade in the SSTA structure index and 7% per decade in the efficiency with which mesoscale turbulent heat-flux anomalies contribute to net eddy-scale air-sea exchange. By reducing cancellation within eddy footprints, the structural shift is also reflected in the eddy-integrated heat-flux contribution, as enhanced positive contributions from anticyclones and enhanced negative contributions from cyclones. A physics-guided attribution analysis links this structural change to strengthened background SST gradients, enhanced eddy trapping, and weakened relative air-sea thermal damping, particularly in western boundary current systems and the Southern Ocean. These results reveal a previously underappreciated, structure-dependent pathway through which mesoscale eddies modulate and amplify eddy-core turbulent heat-flux contribution.