We present self-consistent, non-equilibrium Green's function calculations of the characteristics of short channel carbon nanotube transistors, focusing on the regime of ballistic transport with ohmic contacts. We first establish that the band lineup at the contacts is renormalized by charge transfer, leading to Schottky contacts for small diameter nanotubes and ohmic contacts for large diameter nanotubes, in agreement with recent experiments. For short channel ohmic contact devices, source-drain tunneling and drain-induced barrier lowering significantly impact the currrent-voltage characteristics. Furthermore, the ON state conductance shows a temperature dependence, even in the absence of phonon scattering or Schottky barriers. This last result also agrees with recently reported experimental measurements.