The object of this study is the thermophysical properties of polymer micro- and nanocomposites, as well as the dependence of their heat conductivity with structural characteristics when using different types of fillers. A set of experimental studies of heat conductivity and specific heat capacity of polymer micro- and nanocomposite materials for polyamide 6 and carbon nanotubes, copper and aluminum as matrix and fillers was carried out. When obtaining composites, a method was used that is based on the mixing of components in the polymer melt. The content of fillers varied from 0.3 to 10 %, and the temperature of composite materials – from 305 to 500 K. Experimental dependences of heat conductivity coefficients of the studied composites on the content of the filler were derived. It was established that according to the value of these coefficients in order of their reduction, these composite materials are ranked as follows: composites with fillers with carbon nanotubes, copper, and aluminum. It was found that only one percolation threshold is observed, when using a polyamide 6 matrix. The regularities of changes in the specific heat capacity of the composites under consideration on their temperature when varying within the above limits of the filler content were investigated. The analysis of the influence of the content of fillers on the degree of crystallinity of the polymer matrix of the investigated composite materials was carried out. It is shown that with an increase in the content of fillers, the degree of crystallinity decreases. The relationship between the thermally conductive properties of the composites under consideration and the specified degree of crystallinity has been established. Higher values of heat conductivity of composites correspond to lower values of the degree of crystallinity. The reported results can be widely used in the development of highly heat conductive composites for various engineering applications.