We exploit a microscopically derived master equation for the study of STIRAP in the presence of decay from the auxiliary level toward the initial and final state, and compare our results with the predictions obtained from a phenomenological model previously used [P. A. Ivanov, N. V. Vitanov, and K. Bergmann, Phys. Rev. A 72, 053412 (2005)]. It is shown that our approach predicts a much higher efficiency. The effects of temperature are also taken into account, proving that in b-STIRAP thermal pumping can increase the efficiency of the population transfer.