The thermal conductivity and the structural stability of Bi2Te3 nanowire and nanotubes are investigated by molecular dynamics simulations with growth orientations [0 0 1] [0 1 0]. The thermal conductivity of nanowires is lower than the bulk thermal conductivity by a factor of ten, while for the nanotubes by a factor of twenty. The striking result is that while the nanowires in the direction [001] are dynamically unstable, nanotubes in this direction remain stable. The stability and the ultralow thermal conductivity of Bi2Te3 nanotubes suggest improvement for next thermoelectric generation devices.