We present the first variational calculation of the isotropic hyperfine coupling constant of the carbon-13 atom in the CH3 radical for temperatures T = 0, 96, and 300 K. It is based on a newly calculated high level ab initio potential energy surface and hyperfine coupling constant surface of CH3 in the ground electronic state. The ro-vibrational energy levels, expectation values for the coupling constant, and its temperature dependence were calculated variationally by using the methods implemented in the computer program TROVE. Vibrational energies and vibrational and temperature effects for coupling constant are found to be in very good agreement with the available experimental data. We found, in agreement with previous studies, that the vibrational effects constitute about 44% of the constant's equilibrium value, originating mainly from the large amplitude out-of-plane bending motion and that the temperature effects play a minor role.