  We study quantum population transfer via a common intermediate state
initially in thermal equilibrium with a finite temperature $T$, exhibiting a
multi-level Stimulated Raman adiabatic passage structure. We consider two
situations for the common intermediate state, namely a discrete two-level spin
and a bosonic continuum. In both cases we show that the finite temperature
strongly affects the efficiency of the population transfer. We also show in the
discrete case that strong coupling with the intermediate state, or a longer
duration of the controlled pulse would suppress the effect of finite
temperature. In the continuous case, we adapt the thermofield-based
chain-mapping matrix product states algorithm to study the time evolution of
the system plus the continuum under time-dependent controlled pulses, which
shows a great potential to be used to solve open quantum system problems in
quantum optics.
