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Using transdimensional plasmonic materials (TDPM) within the framework of fluctuational electrodynamics, we demonstrate nonlocality in dielectric response alters near-field heat transfer at gap sizes on the order of hundreds of nanometers. Our theoretical study reveals that, opposite to the local model prediction, propagating waves can transport energy through the TDPM. However, energy transport by polaritons at shorter separations is reduced due to the metallic response of TDPM stronger than that predicted by the local model. Our experiments conducted for a configuration with a silica sphere and a doped silicon plate coated with an ultrathin layer of platinum as the TDPM show good agreement with the nonlocal near-field radiation theory. Our experimental work in conjunction with the nonlocal theory has important implications in thermophotovoltaic energy conversion, thermal management applications with metal coatings, and quantum-optical structures.