An OLED device comprising: a) a substrate; b) one or more OLED light emitting elements located on the substrate and including a first electrode formed on the substrate, one or more OLED light emissive layers located over the first electrode, and a second electrode located over the OLED light emissive layers; c) an encapsulating cover located over the second electrode and affixed to the substrate; and d) a thermally-conductive, conformable, and compressible material in thermal contact with both the OLED light emitting elements and the encapsulating cover over the light emitting area of the OLED light emitting elements, wherein the thermally-conductive material is more than 1 micron thick and has a thermal conductivity greater than 0.25 W/mK.