Medium-energy ion-scattering measurements and Monte Carlo simulations have been used to study the Al(001) surface as a function of temperature. Surface melting does not occur and the surface stays well ordered up to the bulk melting point Tm =933.52 K. The combination of the effective-medium potential, used to simulate the interacting Al atoms, and ion-scattering calculations on the simulated Al(001) surface, reproduces the ion-scattering intensities very well. The Monte Carlo simulations show that the surface relaxations and the vibration amplitudes both display strongly anharmonic behavior which extends several layers into the crystal and increases with increasing temperature.