  We study the heat current flowing between two baths consisting of harmonic
oscillators interacting with a qubit through a spin-boson coupling. An explicit
expression for the generating function of the total heat flowing between the
hot and cold baths is derived by evaluating the corresponding Feynman-Vernon
path integral under the non-interacting blip approximation (NIBA). This
generating function satisfies the Gallavotti-Cohen fluctuation theorem, both
before and after performing the NIBA. We also verify that the heat conductivity
is proportional to the variance of the heat current, retrieving the well known
fluctuation dissipation relation. Finally, we present numerical results for the
heat current.
