"Cold" in astrophysical settings tends to mean T << µ (the chemical potential) which usually justifies a low temperature expansion in T/µ, although thermal effects can be qualitatively important.
> "Cold" in astrophysical settings tends to mean T << µ (the chemical potential)
Yes, I know, but this in itself does not preclude energy being emitted by radiation. To preclude that, the object needs to be in a genuine ground state--no internal transitions possible that can reduce its total energy. That's a considerably stronger condition than T << µ.
