For accurate modelling of observations of exoplanet atmospheres, quantification of the pressure broadening of infrared absorption lines for and by a variety of gases at elevated temperatures is needed. High-resolution high-temperature H2-pressure-broadened spectra are recorded for the CH4 ν3-band P-branch. Measured linewidths for 143 transitions between 2840 and 3000 cm−1 with temperature and pressures ranging between 300 and 655 K, and 10 and 933 Torr, respectively, were used to find rotation- and tetrahedral-symmetry-dependent coefficients for pressure and temperature broadening and pressure-induced lineshifts. The new pressure-broadening data will be useful in radiative-transfer models for retrieving the properties of observed expolanet atmospheres.