Based on the models developed by Lerche et al. (1984) and Pang et al. (1993), an improved model for calculating paleoheat flow into basins is investigated. The new model is an optimization problem with the state variables governed by a thermal conduction equation. A genetic algorithm is used to solve the highly nonlinear optimization problem. As an application, the model is applied to the research into the history of heat flow in the Pearl River Mouth basin located in the South China Sea. The numerical analysis shows that the simulation results are in good agreement with the measured data and indicates that the basin may have undergone three rifting and thermal events. It is also demonstrated that a high R. gradient reflects a response to high paleoheat flow during the early, rapid subsidence stage,while a Iow Ro gradient is a result of the thermal decay during the thermal subsidence because of thermal contraction of a cooling lithosphere.