Partially coherent pulses, especially those with non-Gaussian correlated functions, have rarely been explored in nonlinear media because of the demanding procedure of the widely used coherent-mode representation method. This study develops temporal analogues of the complex screen and phase screen methods, which were recently introduced for the spatial counterpart of a partially coherent beam. These methods were employed to study the beam propagation properties of partially coherent pulses, and the obtained results show that they both are highly precise, convenient, and powerful. We believe that these protocols can effectively provide useful insight into the behavior of many coherence-related phenomena in nonlinear media.