  Using perturbed Bogoliubov equations, we study the linear response to a weak
orbital magnetic field of the heat conductivity of the normal-superfluid
interface of a polarized Fermi gas at sufficiently low temperature. We consider
the various scattering regions of the BCS regime and analytically obtain the
transmission coefficients and the heat conductivity across the interface in an
arbitrary weak orbital field. For a definite choice of the field, we consider
various values of the scattering length in the BCS range and numerically obtain
the allowed values of the average and species-imbalance chemical potentials.
Thus, taking Andreev reflection into account, we describe how the heat
conductivity is affected by the field and the species imbalance. In particular,
we show that the additional heat conductivity due to the orbital field
increases with the species imbalance, which is more noticeable at higher
temperatures. Our results indicate how the heat conductivity may be controlled,
which is relevant to sensitive magnetic field sensors/regulators at the
interface.
