Decreasing the thermal resistance is the critical issue for high-brightness light-emitting diodes. In this paper, the effects of some design factors, such as chip size (24 and 35 mil), substrate material (AlN and high-temperature co-fired ceramic), and die-attach material (Ag epoxy and PbSn solder), on the thermal-dissipation characteristics were investigated. Using the thermal transient method, the temperature sensitivity parameter, $R_{th}$ (thermal resistance), and junction temperature were estimated. The 35-mil chip showed better thermal dissipation, leading to lower thermal resistance and lower junction temperature, owing to its smaller heat source density compared with that of the 24-mil chip. By adopting an AlN substrate and a PbSn solder, which have higher thermal conductivity, the thermal resistance of the 24-mil chip can be decreased and can be made the same as that of the 35-mil chip.