Transport properties of polymer nanocomposites become increasingly important for range applications with many outstanding questions remaining. Thermal conductivity is especially important in applications like temperature sensing and packaging. We chose isotactic PolyPropylene (iPP) as one of the most widely used polymers and created nano-colloidal dispersions at different weight percent concentration of carbon nanotubes (CNTs). We oriented the thin-film samples using melt-shear at 200°C and 1Hz in a Linkam microscope shearing hot stage. Thermal conductivity measurements were performed at room temperature on two iPP/CNT sheared thin-film samples (1% and 5% CNT content) both parallel and perpendicular to the shear direction as well as a pure iPP sheared thin-film, prepared using the same process. Our findings indicate that the CNTs enhance kappa by 12% for the 1% CNT sample and 35% by the 5% CNT sample compared to that measured for pure iPP. Additionally, the CNTs under shear induce a novel anisotropy to the thermal conductivity in iPP/CNTs nano-composites. We introduce an approach to extract the shear induced orientational order of thermal conductivity by the dispersed CNTs.