We use non-equilibrium molecular dynamics (NEMD) to compute the thermal conductivity (κ) of orthogonally ordered cross-bar structures of single-walled carbon nanotubes. Such structures exhibit extremely low thermal conductivity in the range of 0.02-0.07 W m(-1) K(-1). These values are five orders of magnitude smaller than the axial thermal conductivity of individual carbon nanotubes, and are comparable to the thermal conductivity of still air.