The aim of this research is the thermostructural study of Cu-Ti, Cu-Ti 1 vol% multiwall carbon nanotubes (MWCNTs) and Cu-Ti 3 vol% MWCNTs. Several investigation techniques were used to achieve this objective. Dilatometric data show that the coefficient of thermal expansion of the nanocomposite containing less multiwall carbon nanotubes is linear and small. The same nanocomposite exhibits regular heat transfer and weak mass exchange with the environment. Raman spectroscopy shows that the nanocomposite with more MWCNTs contains more defects. This implies that the carbon nanotubes have better dispersion in Cu-Ti 1 vol% MWCNTs. Infrared spectroscopy reveals that Cu-Ti 1 vol% MWCNTs has better crystallinity than Cu-Ti 3 vol% MWCNTs.