= Solution
A collisionless relativistic species redshifts with $T_\nu\propto a^{-1}$. The coupled plasma instead obeys <cosmological entropy conservation>, $g_{*s}T^3a^3=\mathrm{constant}$, and is heated relative to a decoupled species as massive particles annihilate. The <effective number of relativistic energy degrees of freedom> $g_*$ and <effective number of relativistic entropy degrees of freedom> $g_{*s}$ coincide while all species share a common relativistic temperature. Use $g_d:=g_{*s}(T_{\rm dec})\simeq100$ for the <Standard Model> bath, excluding the already decoupled extra species.
Just before ordinary <neutrino decoupling>, the coupled bath contains two <photon> states, four <electron>/<Positron> states and six ordinary <neutrino>/<antineutrino> states. Therefore
$$
g_{*s}=2+\frac78(4+6)=\frac{43}{4}.
$$
The extra-neutrino temperature relative to that bath is then $(43/(4g_d))^{1/3}$. After the ordinary <neutrinos> decouple, <electron>/<Positron> annihilation heats only the <photon> bath: its entropy count changes from $2+(7/8)4=11/2$ to $2$. Both <neutrino> populations miss that last heating, so
$$
\boxed{\frac{T_{\nu,0}}{T_0}=\left(\frac{43}{4g_d}\right)^{1/3}\left(\frac4{11}\right)^{1/3}=\left(\frac{43}{11g_d}\right)^{1/3}\simeq0.34.}
$$
This is the <two-stage entropy dilution of an early-decoupled neutrino>. Numerically \b[$T_{\nu,0}\simeq6.8\times10^{-14}\,\mathrm{GeV}$]. Relative to ordinary relic <neutrinos> it is cooler by $(43/(4g_d))^{1/3}\simeq0.48$.
Let $g_\nu$ count the extra <neutrino>'s populated helicity and antiparticle states. For one conventional <neutrino> plus <antineutrino> species $g_\nu=2$, the same state count as <photons>. The <Fermi-Dirac distribution> supplies the $3/4$ number-density factor, so
$$
\boxed{\frac{n_{\nu,0}}{n_{\gamma,0}}=\frac34\frac{g_\nu}{2}\left(\frac{T_{\nu,0}}{T_0}\right)^3=\frac{3g_\nu}{8}\frac{43}{11g_d}\simeq0.029\frac{g_\nu}{2}.}
$$
Thus a two-state species has about \b[$2.9\%$] of the <photon> number density. Stating $g_\nu$ explicitly also covers a different choice of populated states.
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