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Thermodynamical conditions of beginning dynamical nonlinear processes near the melting point of crystal matters with different type of chemical bond were identified by the technique of digital differential-thermal analysis (DTA). Cooperative pre- and post-melting effects are nonequilibrium phase transitions and can be characterized by the system of thermodynamical parameters J. Introduced system of the parameters characterise of formation specific structure state in a material-mesophase pre- and post-melting. Parameterization of the transient processes during first-order phase transition gives opportunity to investigate influence of different factors, such as initial conditions, heating rate, mass of sample, internal magnetic fields, on mesophase formation.