The inelastic neutron scattering technique has been used to measure phonon frequencies and phonon line shapes in Ar36 at temperatures of 81 K [lattice constant a=5.465(2) A] and 55 K [a=5.440(2) A] primarily along the  and  directions. The 81-K data combined with earlier results for small wave vector by Fujii et al. were fitted to a force-constant model. Detailed comparisons are made of the observed phonon line shapes with those computed from the self-consistent harmonic approximation with added cubic anharmonicity (Glyde and co-workers) and molecular-dynamics simulations (Hansen and Klein). The agreement at high temperatures though still quite satisfactory, was found to be not as good as at low temperatures.