neutron star cooling down?

in nature we dont really have neutrons out and about.

yet, when we observe a dead main sequence small star, we see the its dead body being mostly very hot (10e10 K) neutrons all packed together in a neutron star.

but i cant seem to find information about what happens to the neutrons when they eventually cool down.. i get they are static and dont go though convection to help cooling down, no more fusion, etc... so through what type of quantum radiation do the neutrons lose their energy. they dont have bonded electrons to emit planck rays from...? so what then happens when they lose their bonding energy?

does the neutron star eventually just turn to neutronic dust? or does it happen layer per layerwhile staying basically thermodynamically neutral until its mass runs out?

thank you (im 3rd year Physics undergrad student btw this is for my Cosmo class)