Temperature dependence of the proton spin-lattice relaxation time (T-1) in powdered benzoic acid dimer and in its deuterated analog is calculated. The model assumes that two protons (deuterons) synchronously move in the double-minimum potential of the dimer. The two-dimensional potential energy surface was constructed previously, which adequately describes the static properties of the hydrogen-bonded complex. The important characteristics of this potential are a very strong mode coupling and a very high proton potential barrier (>25 kcal/mol), whereas the experimental activation energy for the proton transfer is known to be on the order of 1 kcal/mol only. This apparent discrepancy is removed by our suggestion that the proton transfer is driven by the transitions between OHO fragment vibrational levels under the action of random forces of the surrounding. The excitation of the low-frequency intermolecular vibrations assists such transfer mechanism strongly. Using four fitting parameters to allow for the medium repolarization, the calculated T-1 temperature dependence is found to be in good agreement with the experiments in the natural and deuterated benzoic acid dimer. The agreement is best at high temperature where the apparent activation energy for proton transfer was found to be 2.3 kcal/mol.