Yes, the Sun's outer layers are not in thermodynamic equilibrium. Bhatnagar and Livingston state, "...different methods of observation yield different values, especially when observations refer to different atmospheric layers."
They show different ways to obtain temperature values, including:
Effective temperature (calculate from total Solar irradiance using Stefan-Boltzmann's law). [They get 5760K, but I have seen 5777K, too.]
Brightness temperature (a Planck temperature. My work shows ~5850K)
Color temperature (UBV filter system)
Kinetic tempeature (derived from average speed of the ions, from P=nkT)
Excitation temperature (from the distribution of energy level comparisons)
Ionization temperature (compares the relative no. of atoms in ionization states)
Then there is the variation in temperature found due to the center-to-limb variation (CLV). This ranges from about 5000K at the limb to about 6400K at the center.
PS
h: Or, in heliochromological terms, from a white limb to a bluish-white center.
