In this paper we show that linear (Debye–Hückel) electrostatic screening is not accurate for solid density, moderate-Z (Z > 10) materials in the hot dense matter regime (T > 100 eV). The disparity between linear and nonlinear descriptions will easily exceed 50%, and in some cases can exceed a factor of two. The effect is most strongly dependent on Z and T with lower temperatures and higher Z favouring stronger nonlinear effects. Our conclusions are reached via fully nonlinear calculations performed using a Poisson–Boltzmann model that has been modified to account for quantum diffraction.