Ultra High Molecular Weight Polyethylene with a reduced number of entanglements can be stretched in the solid state both uni- or biaxially to produce highly oriented tapes and films. The chain orientation, in combination with the reduced number of chain ends, is responsible for the high tensile modulus and tensile strength of the drawn materials, and, as we report here, also for the high thermal conductivity achieved through lattice movements. A property such as thermal conductivity in an electrical insulator makes UHMWPE tapes and films of great applicative interest. In-plane laser-flash thermal analysis has been applied to measure the thermal diffusivity of samples of different molecular weights stretched both uni- and biaxially, and a strong correlation has been found between the drawing ratio and the resulting in-plane thermal conductivity. Values of at least 40 W/m K have been achieved for UHMWPE having Mw comprised between 2 and 10 million, while higher values of 65 W/m K are observed for the higher Mw samples having relatively lesser number of chain ends. Surprisingly the biaxially stretched samples also show in-plane conductivity, with the highest value reaching 18 W/m K, comparable to stainless steel.