A thermally conductive LED assembly is disclosed. The thermally conductive LED assembly includes an elongate conductor cable having a first conductor and a second conductor extending along a length of the elongate conductor cable and a thermally conducting and electrically insulating polymer layer disposed between first conductor and second conductor and a second electrically insulating polymer layer is disposed on the first conductor or second conductor. The electrically insulating polymer layer having a thermal impedance value in a range from 2.5 to 15 C.°-cm2/W and a plurality of light emitting diodes are disposed along the length of the elongate conductor cable. Each light emitting diode is in electrical communication with the first conductor and the second conductor.