The effects of the permittivity anisotropy and size of a nano thin film on its thermal conductivity due to surface phonon-polaritons are studied. We demonstrate that this thermal conductivity is a linear combination of the inverse first and third powers of the film thickness. For a 100-nm-thick film of a-quartz surrounded by air, the thermal conductivity along the optical axis is comparable to the phonon counterpart and equals 13Wm-1K-1, which is 25- higher than that along the perpendicular direction, at room temperature. Higher values are found for thinner films at higher temperatures. © 2014 The Japan Society of Applied Physics.