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In this work the modal decomposition of convective heat transfer distributions in turbulent flows is explored. The organization and thermal footprint of the turbulent flow features generated downstream of wall-proximity two-dimensional square ribs immersed in a turbulent boundary layer are investigated experimentally. This study employs modal decomposition to investigate whether this analysis can allow identifying which characteristics of the flow topology are responsible for the Nusselt-number augmentation, aiming to uncover the underlying physics of heat-transfer enhancement. Heat transfer and flow velocity measurements are performed at a Reynolds number (based on the free-stream velocity and rib side-length) equal to 4600. Square ribs are tested for two different gap spacings from the wall (0.25 and 0.5 ribs side-length) and in wall-attached configuration. A low-thermal-inertia heat transfer sensor coupled with high-repetition-rate Infrared (IR) thermography is designed to study the unsteady variation of the convective heat-transfer coefficient downstream of the obstacles. Flow-field measurements are performed with non-time-resolved Particle Image Velocimetry (PIV). A modal analysis with Proper Orthogonal Decomposition (POD) is applied to both convective heat-transfer maps and velocity-fields. The comparison of the Nusselt-number spatial modes of the clean turbulent boundary layer configuration and of the configurations with the ribs shows a variation of the spatial pattern associated with oscillations with strong spanwise coherence, opposed to the thin elongated streaks which dominate the convective heat transfer in the clean turbulent boundary layer. In configurations where the convective heat transfer is enhanced by coherent structures located close to the wall, similar eigenspectra are observed for both flow field and convective heat transfer modes.