Power dissipation has become a major obstacle in performance scaling of modern integrated circuits, and has spurred the search for devices operating at lower voltage swing. In this letter, we study p-i-n band-to-band tunneling field effect transistors (TFET) taking semiconducting carbon nanotubes as the channel material. The on-current of these devices is mainly limited by the tunneling barrier properties, and phonon scattering has only a moderate effect. We show, however, that the off-current is limited by phonon absorption assisted tunneling, and thus is strongly temperature-dependent. Subthreshold swings below the 60mV/decade conventional limit can be readily achieved even at room temperature. Interestingly, although subthreshold swing degrades due to the effects of phonon scattering, it remains low under practical biasing conditions.