= Thermalization temperature for a massless gauge mediator
{title2=$\Gamma/H=\alpha_Y^2m_{\rm pl}/(1.66\sqrt{g_*}T)$}
A rate proportional to $T$ competes with radiation-era expansion proportional to $T^2$. The interaction-to-expansion ratio therefore grows as the universe cools, crossing unity near $T_{\rm eq}=\alpha_Y^2m_{\rm pl}/(1.66\sqrt{g_*})$. If a phase transition occurs at $T_c\gg T_{\rm eq}$, this high-temperature interaction never establishes <thermal equilibrium> before the transition. Subsequent faster number-changing processes may still establish a thermal distribution; the initial state is not automatically Fermi-Dirac just because the particles are relativistic.
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