  The modelling of quantum heat transfer processes at the nanoscale is crucial
for the development of energy harvesting and molecular electronics devices.
Herein, we adopt a mixed quantum-classical description of a device, in which
the open subsystem of interest is treated quantum mechanically and the
surrounding heat baths are treated in a classical-like fashion. By introducing
such a mixed quantum-classical description of the composite system, one is able
to study the heat transfer between the subsystem and bath from a closed system
point of view, thereby avoiding simplifying assumptions related to the bath
time scale and subsystem-bath coupling strength. In particular, we adopt the
full counting statistics approach to derive a general expression for the moment
generating function of heat in systems whose dynamics are described by the
quantum-classical Liouville equation (QCLE). From this expression, one can
deduce expressions for the dynamics of the average heat and heat current, which
may be evaluated using numerical simulations. Due to the approximate nature of
the QCLE, we also find that the steady state fluctuation symmetry holds up to
order $\hbar$ for systems whose subsystembath couplings and baths go beyond
bilinear and harmonic, respectively. To demonstrate the approach, we consider
the nonequilibrium spin boson model and simulate its time-dependent average
heat and heat current under various conditions.
