This work describes the main findings of a computational fluid dynamics (CFD) analysis intended to accurately investigate the flow field and wall heat transfer as a result of the mutual interaction between a swirling flow generated by a lean burn injection system and a slot–effusion liner cooling system. In order to overcome some limitations of Reynolds-averaged Navier–Stokes (RANS) approach, the simulations were performed with shear stress transport (SST)–scale-adaptive simulation (SAS), a hybrid RANS–large eddy simulation (LES) model. Moreover, the significant computational effort due to the presence of more than 600 effusion holes was limited exploiting two different modeling strategies: a homogeneous model based on the application of uniform boundary conditions on both aspiration and injection sides, and another solution that provides a coolant injection through point mass sources within a single cell. CFD findings were compared to experimental results coming from an investigation carried out on a three-sector linear rig. The comparison pointed out that advanced modeling strategies, i.e., based on discrete mass sources, are able to reproduce the effects of mainstream–coolant interactions on convective heat loads. By validating the approach through a benchmark against time-averaged quantities, the transient data acquired were examined in order to better understand the unsteady behavior of the thermal load through a statistical analysis, providing useful information with a design perspective.