Carbon nanotubes (CNTs) exhibit extraordinary mechanical and thermal properties and as such have become the subject of large research interest. Furthermore, CNTs in a polymer matrix have been shown to significantly enhance the thermal conductivity of the polymer/CNT composite in some cases. A few areas of application for this work are thermal interface materials, thermally conductive composites used in aerospace applications, and polymer heat exchangers. In each of these applications the purpose of the polymer or epoxy is to take advantage of the mechanical properties or chemical inertness. The current issue with their adoption is still the poor thermal conductivity. One approach to overcoming this issue is to embed thermally conductive materials into the host material in low concentrations to enhance the effective thermal conductivity. There has been a significant amount of work in this area, but we are far from an understanding that allows us to design a nanocomposite that gives the desired thermal conductivity (specifically in the high thermal conductivity range). This work explores the role that chemical modification (functionalization) of the CNT can play in tailoring thermal transport properties of the composite under strain. It is expected that the functionalization process would have some effect on conduction between the CNT and the polymer matrix and therefore either increase or decrease the ability of the composite to transport thermal energy. This paper focuses on three different functionalizations of CNT and explores the thermal conductivity of a polymer/CNT composite that uses polydimethylsiloxane (PDMS) as the matrix. The three functionalizations of CNTs considered are that of unfunctionalized, functionalized with a carboxyl group (-COOH), and functionalized with a hydroxyl group (-OH). The CNTs used in this study are strictly multi-walled carbon nanobutes (MWCNTs) purified to 95%. The effect of these three functionalizations on the overall thermal conductivity of the composite is evaluated through experimental methods with a stepped bar apparatus at various levels of strain on the composite sample. Results show that, while functionalization of the CNT may affect the CNT/PDMS bond, the stepped bar apparatus does not provide enough precision on the level of strain placed on the sample for a comparison across functionalizations. Future work will try to elucidate both the effect of strain and functionalization using multiple thermal conductivity measurement techniques.