Exergy analysis is a powerful tool for identifying and quantifying irreversibilities in energy systems, yet its practical application is often hindered by the need to perform iterative calculations of enthalpy and entropy variations for real streams. In this paper, we generalize the concept of thermodynamic overall temperature, defined as T_overall = Δh/Δs between two thermodynamic states. This quantity extends the so-called entropic temperature to characterize any fluid transformation, whether isobaric or involving pressure drops, with or without transfer of work. For an isobaric flow of non-compressible fluid or ideal gas, T_overall reduces to the well-known logarithmic mean temperature. For real stream with pressure variation, its value is expressed in a simple, explicit, and general form, as a function of both the logarithmic mean temperature evaluated at the discharge pressure and an isentropic dissipation factor. This formulation enables the exergy of any real stream to be written in the simple Carnot-like form \( \dot{E}_y = [1 - T_a / \tilde{T}]\dot{Y} \), where\( \dot{Y} \) is the flow energy rate. Based on this unified formulation, we derive explicit expressions for exergy losses and efficiencies for key components, including compressors, turbines, expansion valves, heat exchangers (with and without phase change) and piping sections. Three summary tables synthesize the models according to component type and fluid streams. An extensive validation of models is carried out using the ADVENS Props library for various fluids including water, CO2, propane and ammonia. The maximum relative errors remain exceptionally low: below 0.22% for compressors (mean 0.05%), 0.45% for turbines (mean 0.08%), 0.02% for evaporators (mean 0.01%), and 2.2% for condensers (mean 0.20%), with the valve exhibiting a nearly zero error (machine precision). These results confirm the accuracy and robustness of the explicit formulation for engineering purposes. The proposed framework bridges the gap between classical pinch analysis and real-flow simulation, and the approach is illustrated on typical high-temperature and low-temperature network configurations.