The isovector density wave propagation in symmetric nuclear matter (NM) at finite temperature is studied within the Landau-Vlasov theory. In cold NM a zero sound is found, which is changing to a first sound with increasing temperature. This transition, at variance with the case of a one-component Fermi liquid, does not result in the appearance of a maximum in the attenuation of the collective motion as a function of temperature. The damping width of a volume isovector mode is always monotonically increasing with temperature due to the presence of the collisional friction between neutron and proton liquids. However, a clear effect of the transition is expected on the structure of the dipole response function.The observable consequences of the transition in finite hot nuclei are discussed on the basis of the calculated photoabsorption cross section. The γ-spectra from a thermally excited nucleus 2 0 8 Pb are evaluated within the statistical model using theoretical photoabsorption cross sections and compared to experimental data. A transition temperature T t r ~ 4.5 MeV is deduced.