In this study, we investigated the heat dissipation characteristics of gallium nitride (GaN) high-electron mobility transistors (HEMTs) fabricated on a freestanding GaN substrate (GaN-on-GaN HEMTs) by simulation. Although the GaN substrate has a lower thermal conductivity than the conventional silicon carbide (SiC) substrate, it was demonstrated that the GaN-on-GaN HEMT has a thermal resistance comparable to the conventional GaN-on-SiC HEMT in a simulated structure composed of a 100-mu m-thick substrate and a 2-mu m-thick GaN epitaxial layer. This is because GaN-on-GaN has a higher thermal conductivity of the GaN epitaxial layer and a lower thermal boundary resistance than GaN-on-SiC. Next, the thermal design of a 400-W/eight-channel selective heating microwave oven, which consists of eight pairs of patch antennas and power amplifier (PA) modules, involving a 50-W-class GaN-on-GaN HEMT PA, a driving amplifier, an oscillator, and several circuits, was carried out. The fan and fin specifications and enclosure configuration have been optimized to keep the temperature of the metal base on which the PA modules are mounted below 40 degrees C during full operation. Excellent agreement between the oven thermal simulation and the prototype thermocouple measurements was confirmed for the temperature difference between the metal base and the ambient. Finally, device dimensions for reliable operation were determined by simulating the channel temperature of the GaN-on-GaN HEMT PA during microwave heating. To keep the maximum channel temperature below 200 degrees C, the simulated device layout with a unit gate width (W-gu) of 100-300 mu m and a gate-to-gate spacing (L-gg) of 30-70 mu m was acceptable at a drain efficiency (eta(D)) of 75%. However, appropriate W-gu and L-gg were found to be required with a eta(D) of 65%.