  We study QCD with massless quarks on $\mathbb{R}^3\times S^1$ under
symmetry-twisted boundary conditions with small compactification radius, i.e.
at high temperatures. Under suitable boundary conditions, the theory acquires a
part of the center symmetry and it is spontaneously broken at high
temperatures. We show that these vacua at high temperatures can be regarded as
different symmetry-protected topological orders, and the domain walls between
them support nontrivial massless gauge theories as a consequence of
anomaly-inflow mechanism. At sufficiently high temperatures, we can perform the
semiclassical analysis to obtain the domain-wall theory, and $2$d
$U(N_\mathrm{c}-1)$ gauge theories with massless fermions match the 't~Hooft
anomaly. We perform these analysis for the high-temperature domain wall of
$\mathbb{Z}_{N_\mathrm{c}}$-QCD and also of Roberge-Weiss phase transitions.
