  We show that the local temperature dependence of thermalized electron and
phonon populations along metallic carbon nanotubes is the main reason behind
this non-linear transport characteristics in the high bias regime. Our model
that considers optical and zone boundary phonon emission as well as absorption
by charge carriers is based on the solution of the Boltzmann transport equation
that assumes a local temperature along the nanotube, determined
self-consistently with the heat transport equation. By using realistic
transport parameters, our results not only reproduce experimental data for
electronic transport, but also provide a coherent interpretation of thermal
breakdown under electric stress. In particular, electron and phonon
thermalization prohibits ballistic transport in short nanotubes.
