The thermal design of unmanned satellites and manned spacecraft require the knowledge of heat conduction and radiation of complex geometrical shapes. These complex shapes are usually made up of the more common geometries such as flat rectangular plates, flat polygon plates, triangular plates, cones, disks, parabolas, spheres, cylinders and rectangular boxes known as the nine primitive geometries. The heat transfer conductances have been derived for all the above geometries including circumferential, longitudinal and radial conductances for the non-flat plate type geometries.This paper will present the derivation of the equations for circumferential, longitudinal and radial heat transfer conductance for a right circular thin shell cone or a segment of the cone. A thin shell cone is one in which the radius to thickness ratio is greater than 10. The equations for the surface area of a cone or of a cone segment will also be derived along with the equation to determine the location of the centroid. The surface area is needed to determine the radial conductance in the cone or cone segment and the centroid is needed to determine the heat transfer center of the cone or cone segment for longitudinal conductance. These equations can be used to obtain more accurate results for conductive heat transfer in curved spacecraft components.