Solid He is studied in the pressure and temperature ranges 1-40 TPa and 0-10 000 K using first-principles methods. Anharmonic vibrational properties are calculated within a self-consistent field framework, including the internal and free energies, density-pressure relation, stress tensor, thermal expansion, and the electron-phonon coupling renormalization of the electronic band gap. We find that an accurate description of electron-phonon coupling requires us to use a nonperturbative approach. The metallization pressure of 32.9 TPa at 0 K is larger than found previously. The vibrational effects are large; for example, at P=30 TPa the band gap is increased by 2.8 eV by electron-phonon coupling and a further 0.1 eV by thermal expansion compared to the static value. The implications of the calculated metallization pressure for the cooling of white dwarfs are discussed.