Direct classical trajectories are used to compute energy transfer parameters appropriate for use in master equation calculations for the CH4 reversible arrow CH3 + H reaction in He at 300-2000 K. The quantum chemistry method used in the direct trajectory calculations is MP2/aug'-cc-pVDZ, which is validated against higher level ab initio calculations. The average energy transferred in deactivating collisions is shown to increase with the initial rotational excitation J' of CH4 and with the temperature of the bath gas T-bath. When thermally averaged over J', the resulting average downward energy transfer cc is found to increase nearly linearly with T-bath (alpha = 1107(bath)(0.81) cm(-1)). The results of master equation calculations carried out using the single-exponential-down model and the computed values of alpha are compared with experimental results and recent recommendations. At elevated temperatures (>600 K), good agreement between the predicted and experimental rate coefficients is obtained. At room temperature, the computed rate coefficients are in good agreement with the experimental results if the two-dimensional (E, J) formulation of the master equation is used. Smaller values of alpha (by 25%) are necessary to fit the experimental data at room temperature using the one-dimensional (E) master equation. The present study, combined with previous ab initio transition state theory calculations for the CH3 + H capture rate, provides a complete first-principles characterization of the temperature and pressure dependent rate coefficients for this simple single-well system.