The heating of the bulk of the incident ions at low Mach number quasi-perpendicular collisionless shocks is observed to take place very rapidly, within the shock ramp. In this paper we show that the trajectories of ions passing through the shock ramp lead to a dispersion in phase space resulting in an effective increase in ion temperature. The main heating is predicted to take place in the second half of the ramp. We present results of self-consistent computer simulations which confirm this prediction. ¿ American Geophysical Union 1996