The objective of this work is to realize a numerical modeling of the thermal conductivity of a nano-composite material with polymer matrix: poly methyl methacrylate (PMMA) pigmented with titanium dioxide (TiO₂), and to compare the obtained results with theoretical prediction models and the experimental data as a function of the quenching temperature for TiO₂ fraction equals 3%. For this, a numerical study was conducted using the finite element method to predict the effective thermal conductivity of the nano-composite. In addition, a comparison with the results from the analytical models showed that the proposed numerical model is in good agreement with the analytical models of Hatta and Taya Hashin and Shtrikman for the contact resistance of 10^-3.  In the end the comparison of the numerical model to experimental results based on the quenching temperature shows that all quenching temperatures check the theoretical models of Hashin & Shtrikman and Hatta & Taya.