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In this work, entropy generation analysis is applied to characterize and optimize a turbulent impinging jet on a heated solid surface. In particular, the influence of plate inclinations and Reynolds numbers on the turbulent heat and fluid flow properties and its impact on the thermodynamic performance of such flow arrangements are numerically investigated. For this purpose, novel model equations are derived in the frame of Large Eddy Simulation (LES) that allows calculation of local entropy generation rates in a post-processing phase including the effect of unresolved subgrid-scale irreversibilities. From this LES-based study, distinctive features of heat and flow dynamics of the impinging fluid are detected and optimal operating designs for jet impingement cooling are identified. It turned out that (1) the location of the stagnation point and that of the maximal Nusselt number differ in the case of plate inclination; (2) predominantly the impinged wall acts as a strong source of irreversibility; and (3) a flow arrangement with a jet impinging normally on the heated surface allows the most efficient use of energy which is associated with lowest exergy lost. Furthermore, it is found that increasing the Reynolds number intensifies the heat transfer and upgrades the second law efficiency of such thermal systems. Thereby, the thermal efficiency enhancement can overwhelm the frictional exergy loss.