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 25 years of satellite observations, we show that mesoscale eddy impacts are increasingly shaped by a decadal-scale reorganization of their thermal structure. Globally, eddy-induced sea surface temperature anomalies are shifting toward more coherent, monopole-like configurations, increasing spatial coherence by about 4% per decade and raising by about 8% per decade the efficiency with which mesoscale heat-flux anomalies drive net air-sea exchange. A physically constrained nonlinear attribution analysis shows that this transition arises from strengthened background SST gradients, enhanced eddy nonlinearity, and weakened relative air-sea thermal damping, with the strongest changes in western boundary current systems and the Southern Ocean. However, current high-resolution climate models fail to reproduce this observed shift, suggesting that mesoscale climate feedbacks may be underestimated. These results identify the structural evolution of mesoscale eddies as a previously unrecognized pathway through which climate warming amplifies air-sea heat exchange, with important implications for upper-ocean heat uptake and regional climate extremes.