Hybrid RANS-LES approaches have aroused interest for years since they provide unsteady information at a reduced numerical cost compared to LES. In the hybrid context, the use of temporal filtering, to control the energy partition between resolved and modeled scales, ensures a consistent bridging between RANS and LES models. In this regard, a new formulation of Hybrid Temporal Large Eddy Simulation (HTLES) is developed, aiming at improving the theoretical foundation of the model associated with an eddy-viscosity closure. The analytical development is performed, applying the Hybrid-Equivalence criterion, and the model is calibrated in decaying isotropic turbulence. In addition, an upgraded version of the approach is proposed to improve the behavior of the model in near-wall regions, introducing a two-fold shielding function and an internal consistency constraint to provide a suitable control of the RANS-to-LES transition. Applying HTLES to the k-w-SST model, the validation process is carried out on channel and periodic-hill flows, over a range of grids and Reynolds numbers. The predictive accuracy and the robustness to grid coarsening are assessed in these cases, ensuring that HTLES offers a cost-saving alternative to LES.