The radial heat conduction in the tube wall of dielectric thin tubes is studied in this work. An equation of phonon radiative transfer (EPRT) is used in association with nodal approximation technique for examining the heat transport in the thin tubes. The effective thermal conductivity of thin tubes is calculated based on the heat flux in the middle surface of the tubes. Results indicate that the energy distribution in the annulus is dominated by phonons excited by outer surface. Consequently, the temperature distribution is considerably affected by the temperature of outer surface. In addition to tube wall thickness, R2-R1, which was usually considered as the size effect on heat conduction, the curvature effect would significantly change the heat flux across the tube wall and consequently affect the effective thermal conductivity.