The decay of an ion temperature discontinuity in a collisionless plasma is considered. Theoretical analysis and simulation are used. A shock is formed in the cold plasma region and a rarefaction wave is formed in the hot plasma region. Profiles of density and potential are presented. A comparison of the theoretical dependence on the initial hot ion temperature of the hot ion density, temperature, velocity, current and energy flux at the plateau region and the shock speed with the simulation data shows good agreement.