  We study constraints on thermal phase transitions of ${\rm SU}(N_c)$ gauge
theories by using the 't Hooft anomaly involving the center symmetry and chiral
symmetry. We consider two cases of massless fermions: (i) adjoint fermions, and
(ii) $N_f$ flavors of fundamental fermions with a nontrivial greatest common
divisor ${\rm gcd}(N_c,N_f) \neq 1$. For the first case (i), we show that the
chiral symmetry restoration in terms of the standard Landau-Ginzburg effective
action is impossible at a temperature lower than that of deconfinement. For the
second case (ii), we introduce a modified version of the center symmetry which
we call center-flavor symmetry, and draw similar conclusions under a certain
definition of confinement. Moreover, at zero temperature, our results give a
partial explanation of the appearance of dual magnetic gauge group in
(supersymmetric) QCD when ${\rm gcd}(N_c,N_f) \neq 1$.
