Group III-nitride light-emitting diodes (LEDs) fabricated on sapphire substrates typically suffer from insufficient heat dissipation, largely due to the low thermal conductivities (TCs) of their epitaxial layers and substrates. In the current work, we significantly improved the heat-dissipation characteristics of an InGaN/GaN quantum-well (QW) green LED by using hexagonal boron nitride (hBN) as a heat-transfer medium. Multiple-layer hBN with an average thickness of 11 nm was attached to the back of an InGaN/GaN-QW LED (hBN-LED). As a reference, an LED without the hBN (Ref-LED) was also prepared. After injecting current, heat-transfer characteristics inside each LED were analyzed by measuring temperature distribution throughout the LED as a function of time. For both LED chips, the maximum temperature was measured on the edge n-type electrode brightly shining fabricated on an n-type GaN cladding layer and the minimum temperature was measured at the relatively dark-contrast top surface between the p-type electrodes. The hBN-LED took 6 s to reach its maximum temperature (136.1 degrees C), whereas the Ref LED took considerably longer, specifically 11 s. After being switched off, the hBN-LED took 35 s to cool down to 37.5 degrees C and the Ref-LED took much longer, specifically 265 s. These results confirmed the considerable contribution of the attached hBN to the transfer and dissipation of heat in the LED. The spatial heat-transfer and distribution characteristics along the vertical direction of each LED were theoretically analyzed by carrying out simulations based on the TCs, thicknesses, and thermal resistances of the materials used in the chips. The results of these simulations agreed well with the experimental results.