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Electrically driven thermal light emission (TLE) from individual metallic single-walled carbon nanotubes (mCNTs) is theoretically investigated by detailed simulations and compared to a recent experiment (Mann et al., Nature Nanotech.., vol. 2, p. 33, 2007). The electrical and thermal properties are determined by carrier transport in the metallic subband, which has a zero dipole matrix element and does not experience radiative carrier recombination. The light emission, however, is contributed by the semiconducting subbands, which are populated by a thermal process. The simulation results indicate that due to diameter-dependent thermal effects, the maximum current of suspended mCNTs has a much stronger dependence on the CNT diameter than in non suspended CNTs. The size and shape of the light spot are sensitive to the measured photon energy range. Although the temperature profile along the CNT is approximately parabolic, the light emission profile has a much sharper peak at the middle of the CNT, which is in good agreement with the experiment and confirms the thermal nature of the light emission. The light emission spectrum at high energies is affected by the subband and energy dependences of the radiative recombination lifetime.