The axial thermal conductance of a cylindrical cavity supporting the propagation of hybridized guided modes along its interface with SiO₂ is quantified and analyzed as a function of its radius and mean temperature. In contrast to the well-known radial thermal conductance, we show that the axial one increases with the cavity radius up to 1 cm, in which it takes its maximum that increases with temperature. A maximum thermal conductance of 289.4 nWK⁻¹ is found at 500K, which is more than 3 orders of magnitude higher than the corresponding one found in the far-field regime. This top polariton thermal conductance along the cavity is comparable to the radiative one predicted by Planck's theory and thus represents a fundamental heat transport channel driven by hybridized guided modes able to amplify heat currents along a macroscale cylindrical cavity.