- 2017 American Physical Society. The instability of hot asymmetric nuclear matter with respect to bulk density distortions is considered. The equation of state of the extended Thomas-Fermi approximation is used. The origin of the anomalous dispersion and the influence of the Fermi-surface distortion effects on the bulk and isospin instabilities in homogenous nuclear matter are investigated. It is shown that the development of both instabilities is reduced significantly due to the Fermi-surface distortion effects. The dependence of the bulk instability on the temperature and on the multipolarity of the particle density distortions are shown for the nucleus of Pb208. The dependence of the formation of the decay modes (fission or multifragmentation) of the nuclei on the temperature and the Fermi-surface distortion effects are demonstrated. It is shown that in the case of low temperatures the preferable mode for the bulk instability is binary fission. For higher temperatures, the preferred modes are the multifragmentations for small clusters. The number of clusters increases with increasing temperature.