  We investigate the collective response function and the energy-weighted sums
(EWS) $m_k$ 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. We have evaluated the temperature dependence of the
adiabatic, $E_1=\sqrt{m_1/m_{-1}}$, and scaling, $E_3=\sqrt{m_3/m_1}$, energy
centroids of the isovector giant dipole resonances (IVGDR). The centroid energy
$E_3$ is significantly influenced by the Fermi surface distortion effects and,
in contrast to the isoscalar mode, shows much weaker variation with
temperature. Taking into account a connection between the isovector sound mode
and the corresponding surface vibrations we have established the $A$-dependence
of the IVGDR centroid energy which is 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.
