Power dissipation in electronic devices is projected to increase over the next ten years to the range of 150-250 Watts per chip for high performance applications. One of the primary obstacles to the thermal management of devices operating at such high powers is the thermal resistance between the device and the heat spreader or heat sink that it is attached to. Typically the in situ thermal conductivity of interface materials is in the range of 1 to 4 W/mK, even though the bulk thermal conductivity of the material may be significantly higher. In an attempt to improve the effective in situ thermal conductivity of interface materials nano particles and nanotubes are being considered as a possible addition to such interfaces. This paper presents the results of an analytical and numerical study of transport in a thermal interface material that is enhanced with carbon nanotubes. The results from the analytical model are in excellent agreement with a numerical solution of the same geometry. Wide ranges of parametric studies were conducted to examine the effects of the thermal conductivity of the different materials, the geometry, and the size of the nanotubes. An estimate of the effective thermal conductivity of the carbon nanotubes was used, obtained from a molecular dynamics analysis. The numerical analysis was used to estimate the impact of imperfections in the nanotubes upon the overall system performance. Overall the nanotubes are found to significantly improve the thermal performance of the thermal interface material. The results show that varying the diameter of the nanotube and the percentage of area occupied by the nanotubes doesn't have any significant effect on the total temperature drop.