The present paper is a continuation of the preceding article (Lee et al.) in which it is suggested that the nonadiabatic motion of the directly transmitted ions in a quasi-perpendicular shock wave can result in an increase of the ion kinetic temperature transverse to the ambient magnetic field in the downstream. A series of computer simulations based on a hybrid code have been carried out to examine the dynamics of the transmitted ions in both the subcritical and supercritical shock waves. It is found that in both cases the directly transmitted ions can contribute to the heating process. In the case of a resistiveless supercritical shock the reflected and transmitted ions can be equally important; whereas for a subcritical shock the transmitted ions are primarily responsible for the ion heating. ¿ American Geophysical Union 1987