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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 perturbation estimates and see at high temperatures a tendency towards static configurations. Up to temperatures T similar or equal to 2T(H) we find an indication that tunneling between vacuums with different Chern-Simons numbers is still exponentially suppressed.