  Modeling of thermal transport in practical nanostructures requires making
trade-offs between the size of the system and the completeness of the model. We
study quantum heat transfer in a self-consistent thermal bath setup consisting
of two lead regions connected by a center region. Atoms both in the leads and
in the center region are coupled to quantum Langevin heat baths that mimic the
damping and dephasing of phonon waves by anharmonic scattering. This approach
treats the leads and the center region on same footing and thereby allows for a
simple and physically transparent thermalization of the system, enabling also
perfect acoustic matching between the leads and the center region. Increasing
the strength of the coupling reduces the mean free path of phonons and
gradually shifts phonon transport from ballistic regime to diffusive regime. In
the center region, the bath temperatures are determined self-consistently from
the requirement of zero net energy exchange between the local heat bath and
each atom. By solving the stochastic equations of motion in frequency space and
averaging over noise using the general fluctuation-dissipation relation derived
by Dhar and Roy [J. Stat. Phys. 125, 801 (2006)], we derive the formula for
thermal current, which contains the Caroli formula for phonon transmission
function and reduces to the Landauer-B\"uttiker formula in the limit of
vanishing coupling to local heat baths.
