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Surface waves can lead to intriguing transport phenomena. In particular, surface phonon polaritons (SPhPs), which result from coupling between infrared light and optical phonons, have been predicted to contribute to heat conduction along polar thin films and nanowires [1]. However, experimental efforts thus far suggest only very limited SPhP contributions [2-5]. Through systematic measurements of thermal transport along the same 3C-SiC nanowires with and without a gold coating on the end(s) that serves to launch SPhPs, here we show that thermally excited SPhPs can significantly enhance the thermal conductivity of the uncoated portion of these wires. The extracted pre-decay SPhP thermal conductance is over two orders of magnitude higher than the Landauer limit predicted based on equilibrium Bose-Einstein distributions. We attribute the remarkable SPhP conductance to the efficient launching of non-equilibrium SPhPs from the gold-coated portion into the uncoated SiC nanowires, which is strongly supported by the observation that the SPhP-mediated thermal conductivity is proportional to the length of the gold coating(s). The reported discoveries open the door for modulating energy transport in solids via introducing SPhPs, which can effectively counteract the classical size effect in many technologically important films and improve the design of solid-state devices.