In this study, computational simulations were used to investigate the performance of a carbon-doped boron nitride nanoribbon (BC2NNR) for hydrogen (H2) gas sensing at elevated temperatures. The adsorption energy and charge transfer were calculated when H2 was simultaneously attached to carbon, boron, and both boron and nitrogen atoms. The sensing ability was further analyzed considering the variations in current–voltage (I–V) characteristics. The simulation results indicated that the energy bandgap of H2 on carbon, boron, and both boron and nitrogen exhibited a marginal effect during temperature variations. However, significant differences were observed in terms of adsorption energy at a temperature of 500 K, wherein the adsorption energy was increased by 99.62% of that observed at 298 K. Additionally, the evaluation of charge transfer indicated that the strongest binding site was achieved at high adsorption energies with high charge transfers. Analysis of the I–V characteristics verified that the currents were considerably affected, particularly when a certain concentration of H2 molecules was added at the highest sensitivity of 15.02% with a bias voltage of 3 V. The sensitivity at 298 K was lower than those observed at 500 and 1000 K. The study findings can form the basis for further experimental investigations on BC2NNR as a hydrogen sensor.