Earlier quoted context omitted.
Space is without temperature. Temperature is an attribute of things, space is a lack of things. What you're referring to is the temperature of cosmic background radiation, which is akin to how you emit infrared radiation at your body temperature. But you certainly don't classify the space where this radiation move through as having your body temperature. The two things are not the same imo.
"Temperature" is a slippery word that has many different definitions depending on what area of physics you're working in. In this case it is perfectly fine to refer to "the temperature of space" since you're explicitly using it as a cold sink. As evidence, see the paper (published in Nature no less!) that MengerSponge posted. The authors say "On the other hand, outer space, at a temperature of 3 K, provides a much co…
The space around us is filled with photon coming from Sun at ~5500K, but it doesn't heat anything to anywhere near that. So given the current density of cosmic background radiation at 411 photon cm -3, would it be sufficient to place a blackbody to the equilibrium temperature?
I am not a physicist by training, and this is a genuine question.