Submesoscale eddies (those smaller than 50~km) are ubiquitous throughout the ocean, as revealed by satellite infrared images. Diagnosing their impact on ocean energetics from observations remains a challenge. This study analyzes a turbulent field of submesoscale eddies using airborne observations of surface currents and sea surface temperature, with high spatial resolution, collected during the S-MODE experiment in October 2022. Assuming surface current divergence and temperature are homogeneous down to 30 m depth, we show that more than 80% of the upward vertical heat fluxes, reaching ~227 W~m^{-2}, is explained by the smallest resolved eddies, with a size smaller than 15 km. This result emphasizes the contribution of small-scale eddies, poorly represented in numerical models, to the ocean heat budget and, therefore, to the climate system