This paper presents our results on thermal properties measurements of thermal interface materials based on vertically aligned carbon nanotubes. In this system, the total interface resistance is the sum of thermal resistances created by the contact between the growth surface and the CNTs, the intrinsic resistance of the CNTs array, and the contact between the loose end of the CNTs and the opposite substrate. The latter is reported to be the limiting factor in the optimization of the global interface resistance, and in this work, polymers are used to enhance the thermal contact. Two polymers are studied. It is shown that the use of a polymer as interface material, despite its low thermal conductivity, leads to an improvement of the total thermal resistance. Experimental data and equilibrium molecular dynamics (EMD) show that the thermal contact resistance when using a reactive polymer - able to establish covalent bonds with the CNTs - is at least three times lower than that with the Van der Waals interaction polymer. The reactive polymer also enhances adhesion between CNTs and the polymer, which allows the mechanical complete transfer of the aligned CNTs array from growth substrate to a copper substrate. This transfer process allows to expand applications for VACNTs.