The anharmonic dynamics of a protein molecule was studied by molecular dynamics simulations of the intramolecular vibrational energy transfer in myoglobin. A small excess kinetic energy was added to a specified normal mode, and the process of the energy transfer to other modes was observed. It was found that the vibrational energy was transferred by two distinct mechanisms depending on temperature. Near zero temperature, the vibrational energy is transferred as a process of the Fermi resonance mostly through the third-order coupling terms from one mode to only a limited number of modes, satisfying the resonance condition. As the temperature increases, the resonance-type transfer is dominated by the off-resonance energy transfer through various mode-coupling terms. Near room temperature, the energy transfer involves higher-order coupling terms and indirect processes through intermediate modes in addition to the transfers through the lower-order couplings. In the short-time limit immediately after starting the energy-transfer simulation, we can observe the direct energy transfer between a pair of modes, which shows the dominance of the lower-order coupling terms, and the influence from the dynamic transition at about 180 K.