Impinging jets are essential components of many industrial systems, as liquid rocket engines, electronic cooling devices, paper processing systems and turbomachinery. In practical cases, the jet reaching the target plane is fully turbulent, as heat and mass transfer are maximized in this regime. The flow field generated by the jet impingement is rather complex, as it features a quasi-laminar stagnation region, flow separation, wall jets departing from the stagnation point, and large-scale vortices filling the whole fluid region between the nozzle and the plate. Previous literature works have demonstrated that only high-fidelity computations allow proper modelling of the main flow structures and accurate heat transfer predictions. However, even the results of well-resolved direct numerical simulations show large sensitivity to the choice of the numerical setup. In this work, we carry out high-fidelity simulations of turbulent cooling jets impinging perpendicularly to a solid, isothermal wall. The high-order open-source code Nek5000 is used for the direct numerical simulation of the incompressible Navier-Stokes equations, coupled with a passive scalar equation representing the temperature field. The jet Reynolds number considered in this work is Re= 5300 (based on the bulk jet velocity and the nozzle diameter D), and the nozzle-to-plate distance is H/D=2. We aim at establishing a standardized procedure for the mesh distribution in the wall-parallel and axial directions, and assessing the effects of inflow/outflow conditions on the resulting flow field. More specifically, we emphasize the importance of including the turbulent flow inside the inflow nozzle within the computational domain to obtain physically meaningful results. In addition, we find that the computed heat transfer is strongly dependent on the near-wall grid size and to the choice of the outflow conditions.