  The entropic corrections to the flux-line energy of extreme type-II
superconductors are computed using a schematic dual Villain model description
of the flux quanta. We find that the temperature profile of the lower-critical
field vanishes polynomially at the transition with an exponent $\nu\cong 2/3$
in the isotropic case, while it exhibits an inflection point for the case of
weakly coupled layers in parallel magnetic field. It is argued that vestiges of
these effects have already been observed in high-temperature superconductors.
