After a rapid introduction to the basic physical concepts of radiative heat transfer and the presentation of the general theory valid for arbitrary objects, I will focus on the study of the radiative heat transfer between two identical metallic one-dimensional lamellar gratings. To this aim I will present and exploit a modification to the widely used Fourier modal method, known as adaptive spatial resolution, based on a stretch of the coordinate associated with the periodicity of the grating. I show that this technique dramatically improves the rate of convergence when calculating the heat flux, and that there is a remarkable amplification of the exchanged energy, ascribed to the appearance of spoof-plasmon modes. By comparing our results to recent studies, we find a consistent quantitative disagreement with some previously obtained results going up to 50%.