From the Widom-Kadanoff scaling theory, predictions are made for the temperature and composition dependence of excess enthalpies for binary mixtures. The predictions are tested with one- and two-phase heats of mixing (or excess enthalpies) measured by flow calorimetry for the system C4H9OC2H4OH/H2O over the entire composition range and at temperatures from the lower consolute temperature (T-c) to about 20 degrees C above T-c. Compositions of conjugate phases at each temperature are obtained by solving for points of intersection between fits of the scaling equations to single-phase data and fits of equations for straight lines to two-phase data. The compositions thus obtained are in excellent agreement with literature data. For all but the very highest amphiphile concentrations, the agreement of theory with the data is excellent when a "new" order parameter is used.