The angular distributions and time-of-flight spectra of nearly monoenergetic He atoms with incident energies of 82 meV and 112 meV have been measured after scattering from a clean Cu(001) surface over a large range of crystal temperatures from 100 K to 1000 K. With increasing temperatures the sharp diffraction and phonon peaks of the low temperature quantum regime become broad and featureless as expected for the multiphonon classical regime. The results are compared with a quantum mechanical theory which is able to explain the height, position, width, and area under the multiphonon maximum. In the classical regime, the temperature dependence of the inelastic intensity indicates that the He atoms are reflected by a smooth vibrating barrier presumably due to the surface electron density, and not by a lattice of discrete repulsive surface atomic cores.