I found [1] which reports noise temperatures around 20–30 K for the 34 m antenna that receives Voyager data [2].

The equivalent noise spectral density is around -215 dB/Hz!

[1] https://descanso.jpl.nasa.gov/monograph/series13/DeepCommo_C...

[2] https://voyager.jpl.nasa.gov/mission/science/

Is it possible to keep cooling so we can keep receiving data?

Cooling the LNAs on the earth station? Yes. I doubt the LNA on Voyager is actively cooled.

I wonder if any feed components (prior to LNA) on the earth station are cooled? [1] does not indicate.

Read a paper recently on converting an old NASA earth station with beam waveguide over to a wideband feed. They had to put a rigid waveguide horn on place of the waveguide and actively cool it.