  We study the temperature dependence of the Chern-Simons number fluctuations
in the SU(2) Higgs Model on Euclidean lattices with spatial sizes up to 20^3.
Temperatures well above the Higgs phase transition $T_H$ are achieved on
anisotropic lattices. Numerical results are compared to perturbative results on
finite lattices as well as in continuum perturbation theory. We find
qualitative agreement with perturbative estimates and see at high temperatures
a tendency towards static configurations. Up to temperatures $T \simeq 2T_H$ we
find indication that tunneling between vacuums with different Chern-Simons
numbers are still exponentially suppressed. (Full PostScript file available via
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