The properties of the hydrated electron are studied by quantum-classical molecular-dynamics simulation in a wide range of temperature and pressure, from ambient to supercritical conditions. The calculations are based on a newly developed electron-water pseudo-potential based on rigorous quantum-mechanical calculations in the static exchange limit, as well as a novel methodological approach in which the electron wave function is expanded in a basis set of spherical Gaussians, distributed on a regular cubic lattice. Although the agreement with experiment is not completely quantitative, the strong experimental red shift of the absorption spectrum found experimentally with increasing temperature is recovered and a microscopic interpretation is proposed. It is also demonstrated that the observed shift is a density rather than a temperature effect. Finally, a striking, nonmonotonic evolution of the band width with increasing temperature, or decreasing density, is pointed out. (C) 2003 American Institute of Physics.