The effects of vibrational coherence and vibrational relaxation on the pump-probe stimulated emission are theoretically studied on the basis of the perturbative density operator method and the transient linear susceptibility theory. The time-resolved profiles are simulated for the system with the single vibrational mode at the several temperature at the several probing frequencies. The quantum beats appeared in the profiles are shown to rapidly dephase as the temperature increases. The calculations imply that the time constant of the vibrational relaxation of the intra-dimer mode in the special pair of the D LL mutant od Rhodobacter capsulatus is approximately the order of 300 femtosecond at the low temperatures.