  We investigate the collective response function and the energy-weighted sums
m_k for isovector mode in hot nuclei. The approach is based on the collisional
kinetic theory and takes into consideration the temperature and the relaxation
effects. Taking into account a connection between the isovector sound mode and
the corresponding surface vibrations we have established the A-dependence of
the enhancement factor for the isovector sum rule in a good agreement with
experimental data. We have shown that the enhancement factor for the "model
independent" sum m_1 is only slightly sensitive to the temperature change.
