  We investigate the response function of hot nuclear matter to a small
isovector external field using a simplified Skyrme interaction reproducing the
value of the symmetry energy coefficient.
  We consider values of the momentum transfer corresponding to the dipole
oscillation in heavy nuclei. We find that while at zero temperature the
particle hole interaction is almost repulsive enough to have a sharp (zero
sound type) collective oscillation, such is no longer the case at temperatures
of a few MeV. As a result a broadening of the dipole resonance occurs, leading
to its quasi disappearence by the time the temperature reaches 5 MeV. The
sensivity of the temperature evolution of the width when modifying the residual
interaction strength is also examined.
