  Thermoelectric conductance of an edge mode is investigated. The edge modes of
a $2D $ and $3D$ two band model with parabolic dispersion is considered. For
the the one dimensional non interacting fermions the thermal conductivity
computed agrees with the result known from $Bosonization$ computations. In the
presence of a magnetic field, backscattering is allowed and controls the value
of the thermal conductivity. The thermal conductivity is obtained from the
continuity equation of thermal current energy conservation. The thermal
conductivity is computed introducing the $Scattering$ matrix for particles and
anti-particles. At finite temperatures the backscattering is allowed, the
electric conductance, the thermoelectric conductance and the thermal
conductance decrease with the increase of the magnetic field. At finite
temperatures, weak localization effects are small and can be ignored. We
confirm the experimental results in a magnetic field for a $3D$ Topological
Insulator. An experimental set-up was proposed to test our theory.
