But is there even such a thing as a 'global average temperature'?
Are you asserting that
1) No such thing can be defined, even in principle (implying that it is meaningless to state that the sun is warmer than Pluto,) or that
2) You have in mind some better definition of GAT than those measures currently in use (please share with us, if so..)
Pluto can be considered a frozen ball, although at times it does develop a thin sublimated atmosphere of nitrogen. As a frozen ball it has a temperature.
As for the Sun, we can estimate temperatures at various locations and depths. There certainly is measurable or computable thing that might be called an 'average temperature of the Sun.'
As for the Earth.
Is there an 'average temperature?' I suspect there is at various depths in the crust and in the mantle. But on the surface or slightly below the surface or in the air above the surface? If so, which?
One might attempt the problem in terms of total heat content, but 'average temperature' does not pass muster.