Recent high-dispersion spectroscopy from ground-based telescopes and high-precision spectroscopy from space observatories have enabled atmospheric observations of substellar objects, such as brown dwarfs and hot gaseous exoplanets, with sufficient precision to make ambient gas differences in molecular line broadening a significant factor. In this paper, we experimentally measured the pressure broadening of methane in a high-temperature hydrogen-helium background atmosphere in the H band, which had not been previously measured. The experiment used glass cells, inserted in a tube furnace, filled with methane in a hydrogen-helium background atmosphere or pure methane gas. Spectra were obtained at four temperatures ranging from room temperature to 1000 K, in the wavelength range 1.60-1.63 $\mu$m, using a tunable laser, yielding eight high-resolution spectra in total. A full Bayesian analysis was performed on the obtained spectra, using the differentiable spectral model ExoJAX and the Hamiltonian Monte Carlo for inferring a large number of parameters, allowing us to infer the H2/He pressure broadening for 22 transitions mainly in the R-branch of the 2$\nu_3$ band. As a result, we found a temperature exponent of approximately 0.27 and a reference width at 296 K of around 0.040 for $ J_{lower} $ = 13-20. This temperature dependency is much milder than that provided by the molecular database ExoMol, yielding a line width approximately 5-45% smaller than ExoMol at 296 K, but similar at 1000 K. Our results suggest the need for further accumulation of experimental data for spectral analysis of substellar objects with hydrogen-helium atmospheres.