  We study gauge theories with/without an extra dimension at finite
temperature, in which there are two kinds of order parameters of gauge symmetry
breaking. The one is the zero mode of the gauge field for the Euclidean time
direction and the other is that for the direction of the extra dimension. We
evaluate the effective potential for the zero modes in one-loop approximation
and investigate the vacuum configuration in detail. Our analyses show that
gauge symmetry can be broken only through the zero mode for the direction of
the extra dimension and no nontrivial vacuum configuration of the zero mode for
the Euclidean time direction is found.
