  We introduce the running coupling constant of QCD in the high temperature
phase, $\tilde{g}^2(T)$, through a renormalization scheme where the dimensional
reduction is optimal at the one-loop level. We then calculate the relevant
scale parameter, $\Lambda_T$, which characterizes the running of
$\tilde{g}^2(T)$ with $T$, using the background field method in the static
sector. It is found that $\Lambda_T/\Lambda_{\overline{\text{MS}}}
=e^{(\gamma_E+1/22)}/(4\pi)\approx 0.148$. We further verify that the coupling
$\tilde{g}^2(T)$ is also optimal for lattice perturbative calculations. Our
result naturally explains why the high temperature limit of QCD sets in at
temperatures as low as a few times the critical temperature. In addition, our
$\Lambda_T$ agrees remarkably well with the scale parameter determined from the
lattice measurement of the spatial string tension of the SU(2) gauge theory at
high $T$.
