For Gauss–Bonnet gravity and in the context of holography we show how the thermal DC conductivity can be obtained by solving a generalised system of Stokes equations for an auxiliary fluid on a curved black hole horizon. For more general higher derivative theories of gravity coupled to gauge-fields, we also analyse the linearised thermal and electric currents that are produced by DC thermal and electric sources. We show how suitably defined DC transport current fluxes of the dual field theory are given by current fluxes defined at the black horizon.