  The chromoelectric field generated by a static quark-antiquark pair, with its
peculiar tube-like shape, can be nicely described, at zero temperature, within
the dual superconductor scenario for the QCD confining vacuum. In this work we
investigate, by lattice Monte Carlo simulations of the SU(3) pure gauge theory,
the fate of chromoelectric flux tubes across the deconfinement transition. We
find that, as the temperature is increased towards and above the deconfinement
temperature $T_c$, the amplitude of the field inside the flux tube gets
smaller, while the shape of the flux tube does not vary appreciably across
deconfinement. This scenario with flux-tube "evaporation" above $T_c$ has no
correspondence in ordinary (type-II) superconductivity, where instead the
transition to the phase with normal conductivity is characterized by a
divergent fattening of flux tubes as the transition temperature is approached
from below. We present also some evidence about the existence of flux-tube
structures in the magnetic sector of the theory in the deconfined phase.
