Thermal electron relativistic threshold ($T_{\ast }=m_e{c}^2/k_B$)

In a dilute electron gas, thermal kinetic energies become relativistic near $k_{B}T=m_e{c}^2$, corresponding to $T_{\ast }\simeq 5.93\times 10^9\mathrm{K}$. This is a crossover in the momentum distribution, not an abrupt temperature transition. Degenerate electrons can instead be relativistic at much lower temperature if their Fermi momentum exceeds $m_{e}c$.