The “Water Spider Geometry” (WSG) configuration, representing a newly developed reference test sample designed to suitably investigate the flow and heat transfer processes relevant to cooling systems of internal combustion engines, was computationally investigated by applying a recently proposed Reynolds Stress model called the “Elliptic-Blending Model” (EBM). The WSG configuration resembles a specifically configured pipe geometry that appropriately mimics the flow phenomena encountered in cooling channels of realistic internal combustion engine, such as flow impingement and bifurcation, multiple deflections and flow confluence. The reference database, consisting of mean flow and turbulence fields, was provided by a Large-Eddy Simulation. The EBM formulation has been intensively validated by calculating numerous isothermal wall-bounded flows. The present work focuses on testing the EBM predictive performances under the conditions of non-isothermal flow scenarios. Before proceeding to the WSG configuration, the EBM is pre-validated by computing a jet discharging from a channel-like nozzle and impinging perpendicularly onto a heated wall. The results obtained follow closely the data of the reference Direct Numerical Simulation, also with respect to the predicted second peak at the Nusselt number distribution in terms of different nozzle-to-wall spacing. The EBM-predicted mean velocity field and associated global flow characteristics within the WSG configuration agree well with the results of the reference Large-Eddy Simulation, in contrast to those obtained by the widely used k − ω-SST model, which has been applied in addition. Different treatments of the near-wall region were also used, including integration to the wall and the universal wall-functions. The computationally obtained temperature field evaluated at the WSG walls reveals the hot spot location within a straight pipe segment situated between two deflections, closer to the upstream one, coinciding with the experimentally detected region of most severe degradation caused by intense heating.