A brief review of studies on tile dynamic process of thernml expansion since tile eighties is given. A magnitude of dill'crcnce of one to two orders between the restllts of theoretical calculations and experimental observations of tile characteristic time is discussed. Tile noneqtiilibritnn localized phonon gas in a "'hot spot" is studied using tile Bohzmann equation, leading to a soliton-like solution. It gives tile way to fill the gap of the above-mentioned difference between theory and experiment. Tile lattice relaxation of a laser rod is developed theoretically and verilied experimentally. Different expansion processes of a high-T~ superconductor below and above T< imply the existence of some new features of excitons in the high-T, state.