We report on the design, fabrication, testing and analysis of 4H-SiC bipolar junction transistors with power dissipation density up to 4.9 MW/cm(2) and operation up to 500degreesC. This record power density is attributed to the high thermal conductivity of the SiC and the ability to operate at a high junction temperature. The junction temperature was extracted from the measured common emitter I-V characteristics at ambient temperatures of 35degreesC, 65degreesC and 95degreesC. We found that the junction temperature can be well fitted to a simple heat conduction model and that the measured current gain depends on both the junction temperature as well as the ambient temperature.