In this study we present results of ensemble Monte Carlo simulations for carbon nano-tubes, focusing particularly on semiconducting, single wall, zigzag (n,0) structures of relatively small diameter. The basis for the Monte Carlo simulations is provided by electronic structure calculations in the framework of a tight binding model. The principal scattering mechanism considered is due to the electron-phonon interaction involving longitudinal acoustic and optical phonons. From the ensemble Monte Carlo simulation we determine the electron distribution function as a function of position and time. We explore steady state and transient characteristics. An intriguing result is the oscillatory behavior of the average drift velocity, which we attribute to the optical phonon scattering within the limited phase space of the dynamically one-dimensional band structure.