Monte Carlo (MC) simulation is used to study carrier energy relaxation following thermionic emission at the junction of two van der Waals bonded single-walled carbon nanotubes (SWCNTs). An energy-dependent transmission probability gives rise to energy filtering at the junction, which is predicted to increase the average electron transport energy by as much as 0.115 eV, leading to an effective Seebeck coefficient of 386 μV/K. MC results predict a long energy relaxation length (∼8 μm) for hot electrons crossing the junction into the barrier SWCNT. For SWCNTs of optimal length, an analytical transport model is used to show that thermionic cooling can outweigh parasitic heat conduction due to high SWCNT thermal conductivity, leading to a significant cooling capacity (2.4 × 106 W/cm2).