We have measured the temperature-dependent thermal conductivity κ(T) of boron-carbon-nitride (B-C-N) and boron nitride (BN) nanotube mats. The thermal conductivity of B-C-N nanotubes is phonon dominated and reflects dimensional effect below 70 K. We employ a new analysis method to estimate the intrinsic κ(T) of BN nanotubes converted from B-C-N nanotubes, and find that at room temperature κ(T) of a multiwalled BN nanotube is within 0.04–0.32 times that of a multiwalled carbon nanotube. The lower κ(T) of BN nanotubes than that of carbon nanotubes may be due to the enhanced isotope disorder effect in one dimension.