This work presents a heuristic combining dual variable approximation techniques and the method of successive average to determine the time-varying tolls in a general transportation network. The dual approximation techniques exploit the linear programming structure of the underlying assignment problem which uses the cell transmission model to propagate the traffic dynamics. Both the first best and second best time-varying tolls can be determined in a computationally efficient manner with the proposed heuristic. Numerical experiments are conducted on two networks of different sizes to show the efficacy of the heuristic. From the experiments conducted, the proposed heuristic obtains the solutions with the maximum optimality gap of 2. 03%.