Non-equilibrium radiative heat transport is addressed theoretically within the framework of a stochastic lattice-gas model. We consider a resonating transmission line composed of a chain of radiation resonators, each at a local equilibrium, whose boundaries are in thermal contact with two black-body reservoirs at two different temperatures. In the limit of long chains, the stationary state of the radiation in the transmission line is obtained in a closed form. It exhibits an interesting out-of-thermal-equilibrium behavior, characterized by a non-Planckian energy density and a diffusive energy flux. The latter describes a new type of heat transfer between the reservoirs.