The use of carbon nanotubes (CNTs) as a component of various materials, including polymer-based matrices for polymer nanocomposites (PNCs), to modify ransport properties (electrical and thermal) has generated much research interest due to the wide variety of potential applications form aerospace to microelectronics. Thermal transport enhancement and tailoring has not been as successful as electrical conductivity enhancement, due to differences in electron and phonon transport and limiting mechanisms such as thermal barrier resistance. In this work, aligned multi-walled carbon nanotube (MWNT) forests embedded in a polymer are selected as a controlled and representative element to rigorously study such effects. Alignment of the CNTs along the heat conduction direction optimizes the effective thermal conductivity by minimizing the number of interfaces across the thermal path. Conduction perpendicular to the CNT axis will be studied as well and is dominated by thermal boundary resistance. Heat conduction in the CNT composites at room temperature are also simulated with parameters that describe behaviors at thermal interfaces. The experimental and numerical results are compared to quantify these parameter values for the first time. A significant advantage in our study is the capability to freely change the length and the spacing between the CNTs, and the type of polymer.