The mathematical model for research of thermal properties of composites reinforced by fibers, on datas of thermogravimetric (TG) and differential thermal analyses (DTA) is offered. As against known computational methods of kinetic parameters of destruction materials given macro-kinetic the model of thermal decomposition links time of the process with a contents destructive a component in a material, shape of macromolecules achievable degree of transformation, magnitude of a heat flux, lift velocity of temperature at the expense of an applied heat. As the methods of a derivatography allow defining difference of temperature of an investigated sample from temperature of the environment (DTA), there is a possibility to take into account magnitude of such aberrations immediately in kinetic calculations and by that to reduce influence of this factor at definition of kinetic performances of heterogeneous processes. The model allows utilizing practically information made in the curves of the thermal analysis. If the stages of external and internal diffusion practically do not render a resistance to the process, on chemical reaction does not overlap what padding limitations, and the speed of all heterogeneous process depends only on the kinetic factors. The mathematical model looks like the following: , (1) where E is an activation energy, R is a universal gaseous constant, T is a temperature, ΔT an aberration of temperature at the expense of heat effects of physical and chemical transformations, difiniendum on datas of the differential thermal analysis, В is a coefficient that depends on the molar - volume density and a contents destructive a component in a material, α is a transformation degree, Ψ is a particle size parameter of the shape a macromolecular circuits, Z is a pre-exponential factor, τ is a time, QT = f(T) is a heat equivalent, defined heat flux on a sample or temperature in a reactionary zone. The parameter of the shape is defined on the equation: , (2) where m is a coefficient of elongation a macromolecular circuit. The change of the parameter of the shape of an alternate corpuscle from m represented in the table. Table. Dependence Ψ from m The help of the offered mathematical model defines the thermal properties of composites, on the basis of thermally sound poly (arylat-arylensulfonoxide) of copolymer BCP-7, reinforced by aramide fibers.