The thermal properties of single-walled carbon nanotubes (SWNTs) are of significant interest, yet their dependence on SWNT chirality has been, until now, not explored experimentally. Here, we used electrical heating and infrared thermal imaging to simultaneously study thermal and electrical transport in chirality-sorted SWNT networks. We examined solution processed 90% semiconducting, 90% metallic, purified unsorted (66% semiconducting), and as-grown HiPco SWNT films. The thermal conductivities of these films range from 80 to 370 W m-1 K-1 but are not controlled by chirality, instead being dependent on the morphology (i.e., mass and junction density, quasi-alignment) of the networks. The upper range of the thermal conductivities measured is comparable to that of the best metals (Cu and Ag), but with over an order of magnitude lower mass density. This study reveals important factors controlling the thermal properties of light-weight chirality-sorted SWNT films, for potential thermal and thermoelectric applications.