The in-plane thermal conductance of a vacuum gap supporting the propagation of hybridized guided modes along its interfaces with two polar ${\mathrm{SiO}}_2$ materials is quantified and analyzed as a function of the gap distance and temperature. In contrast to the well-known cross-plane thermal conductance, we show that the in-plane one increases with the gap distance up to 1 cm, in which it takes its maxima that increase with temperature. A maximum thermal conductance per unit width of $103{\text{mW~m}}^{-1}{\mathrm{K}}^{-1}$ is found at 500 K, which is more than 6 (3) orders of magnitude higher than the corresponding one found in the near-field (far-field) regime. This top polariton thermal conductance along the cavity is pretty much equal to the radiative one predicted by Planck's theory and therefore it could be useful to amplify or evacuate heat currents along macroscale gaps.

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• Heat transfer
• Near-field optics
• Optical phonons
• Surface phonon polaritons
• Thermal photovoltaics
• Semiconductors
• Waveguides
• Resonance techniques