We analyse high-field current fluctuations in degenerate conductors by mapping the electronic Fermi-liquid correlations at equilibrium to their semi-classical non-equilibrium form. Our resulting Boltzmann description is applicable to diffusive mesoscopic wires. We derive a non-equilibrium connection between thermal fluctuations of the current and resistive dissipation. In the weak-field limit this is the canonical fluctuation-dissipation theorem. Away from equilibrium, the connection enables explicit calculation of the excess `hot-electron' contribution to the thermal spectrum. We show that excess thermal noise is strongly inhibited by Pauli exclusion. This behaviour is generic to the semi-classical metallic regime.