In the current study, two extreme cases are considered for the dispersion of carbon nanotubes(CNTs) in a polymeric matrix: randomly-oriented and randomly-aligned. The representative volume element (RVE) is used to represent the composite material consisting of epoxy resin matrix and CNT-reinforcement. The finite element method acts as the computational tool to conduct the simulations and investigate the effective parameters, i.e., the influence of the aspect ratio and the orientation, on the thermal conductivity of the matrix. A Fortran subroutine was used for both generation and analysis of the models by means of the MSC Marc finite element package and a Python script was used for the sensitivity analysis. The results indicate that optimum performance of the CNTs in terms of thermal conductivity can be reached by orienting them along the temperature gradient whereas a random distribution improves the conductivity by a smaller magnitude.