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.
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/