A friend posed this question on his facebook and now I’m curious myself. From what I know, two things haven’t been tested yet: 0 Kelvin and a true vacuum.
I’m guessing that since there would be no atoms (or radiation) in a true vacuum, there would be nothing to generate heat. So it would either be 0 Kelvin or no temperature at all since it has nothing to relate to.
Wouldn’t the “ambient temperature” anywhere in the universe be around 2-3 Kelvin (the famous “background radiation” of the Big Bang?)
How you’d (even theoretically) propose to measure the temperature of a space devoid of any matter at all is another question – maybe your suggestion of "undefined’ isn’t completely wrong… However, I think that the Background Radiation also posits a constant flux of energy (photons) everywhere, so I’m not sure…?
Space doesn’t have temperature, matter does. If any objects are located in this vacuum, their temperature will depend on nearby sources of heat.
A vacuum is defined by a lack of matter, not a lack of radiation. So even if you select a region of space with no matter in it, there is still plenty of radiation coursing through that space from matter outside of it.
The level of cosmic background radiation in outer space far from any stars results in objects reaching a steady-state temperature of about 3 Kelvins.
Temperatures very close to absolute zero have been created in a laboratory, but in the absence of human intervention, the lowest you’ll see is going to be the aforementioned 3 Kelvins.
What is the temperature of light?
To me this is as undefined as saying “What is the temperature of an absolute vacume?”
I would expect the effects of virtual particles popping in and out would prevent the existence of a ‘true’ vacuum. That is the absence of everything. Because space itself has properties that obviate the existence of …hmmmm… nonexistence.
Doesn’t it depend on the definition of temperature?
It has always been my understanding that temperature is defined as the average kinetic energy of an atom or molecule. If a space is completely void of atoms/molecules, then can we even talk about temperature? If an electromagnetic wave only exists in the space, is it correct to assign it a temperature value?
The cosmic background radiation does not have a temperature. What it has is a spectrum, and that spectrum matches (rather well) the characteristic spectrum of a black body with a temperature of 2.725K.
If you immersed a perfect black body in the the CMB it would reach equilibrium at a temperature whereby its radiation spectrum matched that of the CMB. Which would mean it too was 2.725K.
I think the OP is more of a thought experiment, asking could the temp be actually referred to as zero, or would it be more proper to say something like the empty set {Ø} ?
Since Kelvin is an actual amount, not an abstract scale like °F or °C, if the mass of a given cubic volume could actually be zero then I believe its temp could be correctly defined as 0 Kelvins. But I don’t know, do Kelvins know when you’re measuring them?!
[nitpick]
Not that I’m much in the nitpicking habit, but they ground this into my brain in Algebra I so thoroughly, I can’t help but regurgitate it at every opportunity. The null (or empty) set is symbolized by either Ø or {} but never as {Ø} as that indicates a non-empty set, namely the set containing the symbol Ø
(How this was going to help solve quadratic equations was less clear, but I guess somehow it did.)
[/nitpick]
ETA: The Algebra I text, BTW, by Dolciani, called this symbol “Phi”. My pre-calc teacher, several years later, was of Greek origin, and he very emphatically ground into our brains that this symbol is NOT the Greek letter Phi. So I’ve got to regurgitate that too. There, I feel so much better now!
Some random thoughts about this.
There is a concept of a photon gas. But it only really seems to work when we consider photons bouncing around inside a container. A container that is a black body has a sea of photons within it that obey a goodly part of the gas laws, (but not the conservation of number.) You can actually do work against the gas. The big difference is that the photons don’t interact with one another (they are bosons - and unless you get some really rare stuff going on they don’t ever interact.) So the only interaction is done when they hit the boundaries of the container. I don’t think it makes sense to consider the CMB flux a photon gas, because it doesn’t have walls to interact with - space expands and the photons have been in flight from not long after the big bang, and will mostly stay in flight until a time we can’t even describe, let alone comprehend.
A box made of a material that is an effective black body, will contain a photon gas, one that exerts pressure on its walls. The temperature of that photon gas is defined
via the spectrum of the radiation, and will the same of the temperature of the walls of the box.
A box sitting in space, will reach equilibrium with the CMB, and the inside walls should reach 2.725K. Thus the space inside the box will also be suffused with a flux of photons with a spectrum identical to the CMB, but this time bouncing around inside the box and arguably now real photon gas.
One might argue that the temperature of an absolute vacuum is the temperature that a physical thermometer would read if it were placed into that vacuum. That would suggest that we might want to consider the photon gas, or in space the CMB.
This allows me to make the wonderful point that you really consider the vacuums environment, it doesn’t make sense to consider the vacuum in a vacuum. 
But that then raises the question about other fluxes. How about neutrinos? What about other bosons? Does a passing gravity wave raise the temperature of a vacuum?
Trouble is, I’m not a physicist, so I just ruminate.