We present a formulation of the nanoscale radiative heat transfer (RHT) using concepts of mesoscopic physics. We introduce the analog of the Sharvin conductance using the quantum of thermal conductance. The formalism provides a convenient framework to analyse the physics of RHT at the nanoscale. Finally, we propose a RHT experiment in the regime of quantized conductance.PACS numbers: 44.40.+a;73.23.-b It has been discovered in the late sixties that the RHT between two metallic parallel plates can be larger than predicted using the blackbody radiation form [1][2][3]. It is now known that this anomalous RHT is due to the contribution of evanescent waves and becomes significant when the distance separating the interfaces becomes smaller than the thermal wavelength λ th = c kBT where is Planck's constant, k B is Boltzmann's constant, c is the light velocity and T is the temperature. Using the framework of fluctuational electrodynamics [4], Polder and van Hove (PvH) were able to derive a general form of the RHT accounting for the optical properties of the media [5]. Since this seminal contribution, several reports have been published in the literature [6][7][8][9][10][11]. A quantum-mechanical derivation [12] has confirmed these results obtained within the framework of fluctuational electrodynamics. While the first papers considered metals, it has been realized that the RHT at the nanoscale can be further enhanced for dielectrics due to the contribution of surface phonon polaritons [13,14]. Recent reviews can be found in Refs. [15][16][17][18].The first attempts to measure a heat flux between metallic surfaces at room temperature and micrometric distances have proved to be inconclusive [19,20]. Experiments in the nanometric regime have clearly demonstrated the transfer enhancement [21,22]. Yet the lack of good control of the tip geometry did not allow quantitative comparison with theory. More recent experiments [23,24] are performed using silica taking advantage of the flux enhancement due to the resonant contribution of surface phonon polaritons. A good agreement between PvH theory and experiments has been reported [24].The purpose of this paper is to establish a link between the PvH form of the radiative heat flux and the formalism of transport in mesoscopic physics. It will help to develop a more physical understanding of the RHT at the nanoscale, which also clarifies how losses and non-local effects determine the maximal achievable heat flux [10]. Finally, we will show that this reformulation raises the prospect of observing quantized conductance for systems with sizes on the order of the thermal wavelength λ th .We start our discussion with the PvH form of the RHT. We consider a vacuum gap with width d separating two homogeneous half spaces labeled medium 1 and 2 [see Fig. 1 a)]. Then, the heat flux is [5,16] ( 1) where κ = (k x , k y ) and γ = k 2 0 − κ 2 are the parallel and normal wave vector, Θ(ω,is the mean energy of a harmonic oscillator, k 0 = ω/c, r 1,2 j are the usual Fresnel factors for s-or p-polar...