We present traceable three-parameter extended Hückel equations for the activity coefficient of sodium chloride and for the osmotic coefficient of water in aqueous NaCl solutions from 273.15 to 373.15 K. In this temperature range, our equations seem to apply within experimental error to all thermodynamic data available for these solutions up to the molality of the saturated solution. Our previous studies (J. Chem. Eng. Data 2017, 62, 2617-2632 and 2019, 64, 16-33) showed that, from 273.15 to 373.15 K, two-parameter Hückel equations can successfully explain the literature results of electrochemical, isopiestic, and cryoscopic measurements at least up to a molality of 0.2 mol·kg-1. The model recommended in this study employs the values of our previous two-parameter model for the ion-size parameter in the original Debye-Hückel equation, B, and for the coefficient of the linear term with respect to the molality, b1. In addition, it includes a quadratic term with respect to the molality with the coefficient b2. Both b1 and b2 are quadratically dependent on temperature. With the introduction of b2, our model is able to explain the existing vapor pressure, electrochemical, and solubility data from 273.15 to 373.15 K up to the saturated solution. A comparison with the most important literature values for the activity and osmotic coefficients revealed that the agreement is always at least satisfactory, but is best for temperatures below 363 K. On the basis of these results, our activity and osmotic coefficients are the most reliable values for these thermodynamic quantities so far. We propose this is true also for the values from 363 to 373 K.