  The two-dimensional U(1)-gauged Higgs model is studied on an euclidean
lattice of size $L_1\times L_2$, where the temperature $T=L_2^{-1}$ is of the
order of the sphaleron mass. The simulation parameters are taken from zero
temperature results. By comparison with classical and semiclassical results I
discuss, whether the sphaleron transition rate can be extracted from the
behavior of the Chern-Simons number and from the formation of vortices in an
euclidean simulation at high temperatures.
