The thermal conductivity of nanocomposite polymer materials based on polyvinyl alcohol and epoxy resin with the inclusion of multi-walled carbon nanotubes was studied using the laser flash method. The possibility of using the laser flash method to determine thermal conductivity in thin-film polymer materials is demonstrated and its features are revealed. It has been shown that the presence of carbon nanotubes in polymer matrices leads to an increase in the coefficients of thermal diffusivity and thermal conductivity by several times compared to pure polymer materials.