  We focus on the non-equilibrium two-bath spin-boson model, a toy model for
examining quantum thermal transport in many-body open systems. Describing the
dynamics within the NIBA equations, applicable, e.g., in the strong system-bath
coupling limit and/or at high temperatures, we derive expressions for the
cumulant generating function in both the markovian and non-markovian limits by
energy-resolving the quantum master equation of the subsystem. For a markovian
bath, we readily demonstrate the validity of a steady-state heat exchange
fluctuation theorem. In the non-markovian limit a "weaker" symmetry relation
generally holds, a general outcome of microreversibility. We discuss the
reduction of this symmetry relation to the universal steady-state fluctuation
theorem. Using the cumulant generating function, an analytic expression for the
heat current is obtained. Our results establish the validity of the
steady-state heat exchange fluctuation theorem in quantum systems with strong
system-bath interactions. From the practical point of view, this study provides
tools for exploring transport characteristics of the two-bath spin-boson model,
a prototype for a nonlinear thermal conductor.
