We show that the local temperature dependence of thermalized electron and phonon populations along metallic carbon nanotubes is the main reason behind the nonlinear transport characteristics in the high bias regime. Our model is based on the solution of the Boltzmann transport equation considering both optical and zone boundary phonon emission as well as absorption by charge carriers. It also 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.