The presented results are for the numerical verification of a method devised to identify an unknown spatio-temporal distribution of heat flux that occurs at the surface of a thin aluminum plate, as a result of pulsed laser beam excitation. The presented identification of boundary heat flux function is a part of the newly proposed laser beam profiling method and utilizes artificial neural networks trained on temperature distributions generated with the ANSYS Fluent solver. The paper focuses on the selection of the most effective neural network hyperparameters and compares the results of neural network identification with the Levenberg–Marquardt method used earlier and discussed in previous articles. For the levels of noise measured in physical experiments (0.25–0.5 K), the accuracy of the current parameter estimation method is between 5 and 10%. Design changes that may increase its accuracy are thoroughly discussed.