  The dual superconductivity is a promising mechanism for quark confinement. We
have proposed the non-Abelian dual superconductivity picture for SU(3)
Yang-Mills theory, and showed the restricted field dominance (called
conventionally Abelian dominance), and non-Abelian magnetic monopole dominance
in the string tension. We have further demonstrated by measuring the
chromoelectric flux that the non-Abelian dual Meissner effect exists and
determined that the dual superconductivity for SU(3) case is of type I, which
is in sharp contrast to the SU(2) case: the border of type I and type II.
  In this talk, we focus on the confinement/deconfinement phase transition and
the non-Abelian dual superconductivity at a finite temperature: We measure the
Polyakov loop average and correlator and investigate the restricted field
dominance in the Polyakov loop. Then, we measure the chromoelectric flux
between a pair of static quark and antiquark created by a pair of Polyakov
loops, and investigate the non-Abelian dual Meissner effect and its relevance
to the phase transition.
