The vibrations of ions in solids at finite temperature depend on interatomic force-constants that result from electrostatic interactions between ions, and the response of the electron density to atomic displacements. At high temperatures, vibration amplitudes are substantial, and electronic states are affected, thus modifying the screening properties of the electron density. By combining inelastic neutron scattering measurements of Fe1-xCo xSi as a function of temperature, and finite-temperature first-principles calculations including thermal disorder effects, we show that the coupling between phonons and electronic structure results in an anomalous temperature dependence of phonons. The strong concomitant renormalization of the electronic structure induces the semiconductor-to-metal transition that occurs with increasing temperature in FeSi. Our results show that for systems with rapidly changing electronic densities of states at the Fermi level, there are likely to be significant phonon-electron interactions, resulting in anomalous temperature-dependent properties.