Spectra of hot methane were recorded using a tube furnace and a high-resolution Fourier transform spectrometer. We obtained experimental absorption spectra in the 1.85-1.11um near-infrared region at eight temperatures ranging from 295K up to 1000K. We have converted these into an atlas of absorption cross sections at each temperature for the methane tetradecad, icosad and triacontad polyads, excluding some spectral intervals either strongly contaminated by water or due to baseline fringes. On the theoretical side, the spectra were simulated from the ab initio-based Reims-Tomsk TheoReTS line list for the same experimental conditions. This line list has been constructed by global variational calculations from potential energy and dipole moment surfaces followed by empirical line position corrections deduced from previously published analyses. The comparisons showed very good overall agreement between observations and theory at high spectral resolution for the tetradecad and icosad and at medium or low resolution above this range. A full set of the theoretical absorption cross sections is also included. Detailed temperature dependence of the methane absorption enables the efficient method of remotely probing the temperature of distant astronomical objects based on a comparison of relative signals in carefully selected spectral intervals. This first combined experimental and theoretical easy-to-use cross-section library in the near-infrared should be of major interest for the interpretation of current and future astronomical observations up to a resolving power of 100000-300000 in the range 6400-7600cm^-1^ and a resolving power of 5000-10000 in the higher wavenumber range up to 9000cm^-1^.