Why has the neutrino cosmic background a lower temperature than the cosmic background radiation?

Does the neutrino gas pervading the universe (cosmic neutrino background, CNB) always have the same temperature? Does it still have the temperature as the neutrino gas that emerged from the big bang? Neutrinos don’t interact, so how could the gas be cooled down (apart from space expansion)?

When the CNB came into existence, one second after the big bang, the universe had a temperature of $10^{10}$ Kelvin. So the neutrino gas was at this temperature too. It is said that the CNB nowadays has a temperature of about $1,9$ Kelvin. This is lower than the CMBR, the photon gas that’s permeating the universe, which has a temperature of about $2,7$ Kelvin. The photon gas came somewhat later in existence. About $380 000$ years after the big bang. Which can be seen as the same time, on a cosmic scale (or not?). The universe had a temperature of about $3000$ Kelvin at that time. As space has expanded for both the CNB and CMBR by the same amount, then why has the CNB a lower temperature than the CMBR, which was created when the temperature of the universe was much lower than when the CMBR was created.