  We consider the Ginzburg-Landau heat flow on the two-dimensional flat torus,
starting from an initial data with a finite number of nondegenerate zeros --
but possibly very high initial energy. We show that the initial zeros are
conserved and the flow rapidly enters a logarithmic energy regime, from which
the evolution of vortices can be described by the works of Bethuel, Orlandi and
Smets.
