Also no perfect vacuum exists which renders this rather irrelevant for discussing what happens in real situations. I also did some reading to figure out the correct terminology - it is certainly correct to say that a perfect vacuum has no thermodynamic temperature as it is defined by the state of motion of the particles making up the system you want to assign a temperature to, however I am still not convinced that it is wrong to associate a temperature with a vacuum based on the electromagnetic radiation filling it.
You keep repeating a point I never disagreed with, a perfect vacuum has no thermodynamic temperature. My issue with that is that I think it is a too narrow viewpoint for the comment I initially replied to. If one understands temperature as what a thermometer measures, then the temperature of a vacuum will be the temperature of its walls, it will not magically show »undefined« because you insist that temperature means thermodynamic temperature.
You say you don't disagree but you keep disagreeing...
I made a simple, yet fundamental statement. It's either true or false. There is no need to argue as if you had to out-do me in any way.
Vacuum cannot have a temperature. This follows immediately from the definitions.
This also means that the temperature of a vacuum's "walls", by which I'm guessing you mean particles in 'contact' with the vacuum, is just the temperature of these particles. It's not an indication of any "vacuum temperature".
Vacuum cannot have a temperature, by the definition you are using. This makes it useless for certain tasks, such as determining the temperature an object within a vacuum will stabilize at over time. Thus, we use a different definition of temperature - because saying 'the temperature an object will stabilize at' every time instead of 'temperature' is really wordy.
You seem to agree with me since you explain how 'temperature' may be assigned to vacuum as a fudge. This is a dangerous thing to do as equilibrium temperature does not depend on the vacuum itself but on any radiations present.
Try to look up the definition of temperature and you will see that it is not as simple as you think. One possible definition defines temperature as the partial derivative of the internal energy with respect to the entropy. Why wouldn't that be applicable to an ideal vacuum or a radiation-filled vacuum? Maybe it is not, I am neither a physicist nor particularly knowledgeable in thermodynamics and statistical mechanics, but it is - at least to me - not obvious that it is not applicable. There are also generalized definitions of temperature applicable to system of few particles, i.e. not relying on the statistics of many-particle systems, which sounds like it should be applicable to any real vacuum as any real vacuum will never be perfectly empty.
