  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 to the periodicity
of the grating. We first show that this technique dramatically improves the
rate of convergence when calculating the heat flux, allowing 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 disagreement with some previously obtained results going up to
50\%. In some cases, this disagreement is explained in terms of an incorrect
connection between the reflection operators of the two gratings.
