We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasi-harmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the temperature dependence of other material properties governed by it.