Knowledge of thermal conductance of carbon nanotubes under mechanical deformation is important to characterize the robustness of carbon nanotube heat conduction. In this study, using molecular dynamic simulations, we have calculated thermal conductance of an elastically buckled single-walled carbon nanotube. A local buckle was formed by mechanically bending a carbon nanotube at an angle of 60°, and thermal conductance through the buckle was calculated by a nonequilibrium molecular dynamics approach. The thermal conductance exhibits strong diameter dependence, correlated with the strain energy generated in the buckle. Despite the highly stained deformation, the thermal resistance across a buckle is similar to that of a point defect and heterotube junction, revealing a robust nature of carbon nanotube heat conduction to buckling deformation. *shiomi@photon.t.u-tokyo.ac.jp