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We calculate the radiative heat transfer between two identical metallic one-dimensional lamellar gratings. To this aim we 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. We first show that this technique dramatically improves the rate of convergence when calculating the heat flux, allowing us to explore smaller separations. We then present a study of heat flux as a function of the grating height, highlighting a remarkable amplification of the exchanged energy, ascribed to the appearance of spoof-plasmon modes, whose behavior is also spectrally investigated. Differently from previous works, our method allows us to explore a range of grating heights extending over several orders of magnitude. By comparing our results to recent studies we find a consistent quantitative …