Finite temperature SU(2) lattice gauge theory is investigated in a 3D cubic
box with fixed boundary conditions (b.c.) provided by a discretized, stati
c BPS monopole solution with varying core scale mu. For discrete mu-values
we find stable classical solutions either of electro-magnetic ('dyon') or o
f purely magnetic type inside the box. Near the deconfinement transition we
study the influence of the b.c. on the quantized fields inside the box. In
contrast to the purely magnetic background field case, for the dyon case w
e observe confinement for temperatures above the usual critical one.