  We investigate the deconfining phase transition in QCD_4 and QED_4 at finite
temperature using a perturbative deformation of topological quantum field
theory (TQFT). A modified maximal abelian gauge (MAG) is utilized in the
analysis. In this case, we can derive the linear potential studying the 2D
theory through Parisi-Sourlas (PS) dimensional reduction. The mechanism of
deconfining phase transition is proposed. It is geometrical to discuss the
thermal effect on the linear potential. All we have to do is to investigate the
behavior of topological objects as such instantons and vortices on a cylinder.
This is the great advantage of our scenario. This mechanism is also applied in
the case of QED_4. The phase structure at the high temperature of QED is
investigated using the Coulomb potential on a cylinder. It coincides with the
result in the lattice compact U(1) gauge theory. Also, QCD with MAG has the
property called the abelian dominance, which enables us to discuss the
deconfinement of QCD_4.
