We report on evaluations of local heating in Au single-atom chains at room temperature. We performed onsite thermometry of atomic-scale Au junctions under applied sinusoidal voltage of variable amplitudes. The AC approach enabled to preclude electromigration effects for characterizing the influence of energy dissipations on the lifetime. We elucidated nonlinear increase in the effective temperature of the current-carrying single-atom chains with the voltage amplitudes, which was attributed to subtle interplay between electron-phonon scattering and electron-mediated thermal transport in the quasi-ballistic conductor. We also found that only 0.2% of the electric power contributed to local heating while the majority was consumed at the diffusive bank. The present findings can be used for thermal management of future integrated nanoelectronics.