An enabling advantage of carbon-based conductors is their low density and high thermal conductivity. To put this in the perspective of applications, current rating of carbon-based and copper nanocomposite conductors of different lengths are modeled. For comparison, the current and current density required to raise the maximum temperature of studied conductors to are calculated with a joule heating model. The model is validated with an experimental setup equipped with a thermal camera. It is shown that while doped carbon nanotube (CNT) conductors may potentially result in improved performance compared with copper on a weight basis, ultra-conductive copper (UCC) can outperform copper on both volume and weight bases. Additionally, a hypothetical copper-matrix composite conductor with different volume fractions of high thermal conductivity and lightweight graphene fibers (Cu–C composite) is included in the analysis. The properties of the Cu–C composite are evaluated based on the Lewis–Nielson and rule of mixture models, as inputs for the joule heating model. The results show that while the improved thermal conductivity of the composite is beneficial for improving the current rating in micro-electronics applications, the tradeoff for the decreased electrical conductivity results in lower current carrying capacity in applications that use longer conductors.