We present a study of vertically suspended smectic films under the influence of temperature gradients in the film plane. It is shown that such gradients lead to the transport of smectic material, even against the action of the gravitation forces, from the hot to the cold film edge, In addition, we observe thermally driven convection in these films, and it is demonstrated that the surrounding air plays an essential role for this instability. We compare this result with convective patterns in soap films reported by Martin and Wu in Phys. Rev. Lett, 80 1892 (98) and give some evidence that their interpretation has to be modified, the contact with surrounding air has to be taken into account.