The Earth is just plain not in thermodynamic equilibrium.
Technically correct, because the earth has a hot core. But the geothermal flux (0.09 W/M2) is miniscule compared with mean solar irradiance (341.3 W/M2). So how is this relevant? As to whether Pluto's core is significantly warmer than its surface, I don't honestly know.
The Sun is a gas ball and it's dynamics are shown by the virial theory.
Virial theory?! There is a virial theor
em--but it applies to quasi-spherical collections of freely co-orbiting bodies (e.g. elliptical galaxies or open clusters.) It says nothing about densely packed balls of matter with small mean free path.
Sure there are some uses for temperature measurements, but attempting to build a number for a 'global average temperature' has no meaning. You might as well average all the numbers in a telephone book.
Poor example. Telephone numbers do not encode the value of any parameter, rather they are merely arbitrary routing addresses. So of course their average is meaningless. It does not follow that temperatures (which do encode the value of a parameter) cannot be meaningfully averaged.
All this aside, I would submit that one could refer to "temperature at the gas/liquid and gas/solid interfaces" or to "air temperature two meters above said interfaces" in a perfectly consistent manner. These are not the same numbers, to be sure, but they are far from uncorrelated, and they tend to show similar historical trends.
The virial does relate to the apparent size and temperature of the Sun, a ball of gas. If it were hotter, it expands (of course dependent on plasma ion molecular weight). Same actually occurs with the Earth, if the gas envelope got hotter it would expand. Half the molecular energy into kinetic, half into potential, larger gas ball surface area for radiating heat outward, etc.
All this aside, I would submit that one could refer to "temperature at the gas/liquid and gas/solid interfaces" or to "air temperature two meters above said interfaces" in a perfectly consistent manner. That would be true for a regional section in my opinion. Say a hundred square mile piece of the Sahara. A chunk of Antarctica. A midwest section of farmland perhaps.
But mix up terrain, water mass, ice mass, and you have a mess. Plus you never had the alleged "air temperature two meters above the surface".
But yeah, re your conclusion, the closest we could get to actually talking about a 'global temperature' would be polar orbiting satellite. Reading microwave radiation from oxygen in the air. Or go further out and just read albedo of the planetary disk. Doing either for extended periods of time (decades) introduces instrument error issues.