The interfacial thermal resistance of pristine and defective carbon nanotubes (CNTs) embedded in low-density polyethylene matrix is studied in this paper. Interface thermal resistance in nanosystems is one of the most important factors that lead to the large variation in thermal conductivities in literature and the novelty of this paper lies in the estimation of the interfacial thermal resistance for defective nanotubes-systems. Thermal properties of CNT nanostructures are estimated using molecular dynamics (MD) simulations and the simulations were carried out for various temperatures by rescaling the velocities of carbon atoms in the nanotube. This paper also deals with the mesoscale thermal conductivities of composite systems, using effective medium theories by considering the size effect in the form of interfacial thermal resistance and also using the conventional micromechanical methods like Hashin-Shtrikman bounds and Wakashima-Tsukamoto estimates.