  We study SU(2) gluodynamics at finite temperature on both sides of the
deconfining phase transition. We create the lattice ensembles using the
tree-level tadpole-improved Symanzik action. The Neuberger overlap Dirac
operator is used to determine the following three aspects of vacuum structure:
(i) The topological susceptibility is evaluated at various temperatures across
the phase transition, (ii) the overlap fermion spectral density is determined
and found to depend on the Polyakov loop above the phase transition and (iii)
the corresponding localization properties of low-lying eigenmodes are
investigated. Finally, we compare with zero temperature results.
