  Winding number transitions in the two dimensional softly broken O(3)
nonlinear sigma model are studied at finite energy and temperature. New
periodic instanton solutions which dominate the semiclassical transition
amplitudes are found analytically at low energies, and numerically for all
energies up to the sphaleron scale. The Euclidean period beta of these finite
energy instantons increases with energy, contrary to the behavior found in the
abelian Higgs model or simple one dimensional systems. This results in a sharp
crossover from instanton dominated tunneling to sphaleron dominated thermal
activation at a certain critical temperature. Since this behavior is traceable
to the soft breaking of conformal invariance by the mass term in the sigma
model, semiclassical winding number transition amplitudes in the electroweak
theory in 3+1 dimensions should exhibit a similar sharp crossover. We argue
that this is indeed the case in the standard model for M_H < 4 M_W.
