I recently had a discussion where we did not come to a conclusion because of several seemingly equivalently good arguments that contradicted each other. Maybe someone can help here.
Suppose we have an object (a satellite, or maybe just a rock) in deep space. We assume that the only relevant interaction is with the cosmic background radiation that can be described as a black body radiation of roughly $T_b\approx 3K$. No heating up from stars, no friction due to stellar gas molecules, just the background radiation.
The question is: Would the object eventually have a temperature of the background radiation, i.e. $T\rightarrow T_b$?
On the one hand, it seems that the background radiation is kind of a (near-infinite) thermal bath, and any object in a thermal bath will eventually have the temperature of the bath.
On the other hand, the assumption that the background radiation can be viewed as a bath in equilibrium seems questionable. If I understood it correctly, the homogeneity of the radiation stems from a situation shortly after the Big Bang where the universe was very uniform, which is not the case anymore, so I am not sure if the typical rules of a thermal bath apply.
What would happen with the temperature of such an object?
