In Part I and II of this three-part tutorial on dual-functional radar-communication (DFRC) design for vehicular networks, we overviewed the basics of radar and communication systems and the state of the art in DFRC respectively. As Part III of the tutorial, we address the issue of predictive beamforming for the vehicle-to-infrastructure (V2I) links without the need for explicit state evolution models. The beam tracking is done with the aid of the dual-functional radar-communication signals transmitted by the road side unit (RSU). The vehicle's location parameters are estimated by exploiting the reflected echoes signals. Given these estimates, we propose a prediction method to predict the next position of the vehicle, without specifying a state model. Finally, we verify the superiority of the proposed approaches via numerical simulations, which show that the proposed technique outperforms the conventional benchmark schemes in terms of the achievable communication rate.