  Five-dimensional $SU(3)$ gauge-Higgs unification models are studied at finite
temperature in the warped extra dimension $S^1/\mathbb{Z}_2$. In order to
investigate the phase structure, we developed a technique to compute the
one-loop effective potential with the nontrivial Polyakov loop phase and with
the nontrivial Wilson line phase along the extra dimension. Effective
potentials as functions of two gauge-field condensations are shown for several
simple matter contents, including fundamental, sextet, and adjoint
representational Dirac fermions. Possible extensions and applications of our
formalism are also briefly discussed.
