Spatially resolved heat-transfer predictions in ribbed cooling channels require expensive CFD simulations, limiting design exploration. We present a reduced-order framework that reconstructs temperature and heat-transfer coefficient fields using proper orthogonal decomposition trained on high-fidelity CFD data. Separate bases and Gaussian process models are constructed for six rib and guide-vane families. Wall heat flux is recovered from near-wall gradients and corrected using percentile maps with design-dependent blending derived from leave-one-out reconstructions. Across 24 unseen validation cases, 29–30 modes retain 95% of the snapshot energy and normalized temperature errors remain below 26%. The correction reduces heat-flux errors across most validation sections while preserving dominant spatial structures. Normalized Nusselt-number fields reproduce rib-and bend-induced patterns, with larger discrepancies in demanding bend regions. Online predictions require 9–19 s and reduce marginal CPU cost by three to four orders of magnitude relative to CFD, enabling rapid thermal assessment within the sampled design space.