  Finite temperature SU(2) lattice gauge theory is investigated in a 3D cubic
box with fixed boundary conditions provided by a discretized, static BPS
monopole solution with varying core scale $\mu$. Using heating and cooling
techniques we establish that for discrete $\mu$-values stable classical
solutions either of self-dual or of pure magnetic type exist inside the box.
Having switched on quantum fluctuations we compute the Polyakov line and other
local operators. For different $\mu$ and at varying temperatures near the
deconfinement transition we study the influence of the boundary condition on
the vacuum inside the box. In contrast to the pure magnetic background field
case, for the self-dual one we observe confinement even for temperatures quite
far above the critical one.
