The paper presents the results of thermal modeling of a half-bridge monolithic integrated circuit (IC) with integrated drivers and enhanced mode power high electron mobility transistors, based on a GaN-on-SOI heterostructure. It had been established that the main heat sources in the IC were the half-bridge GaN HEMTs. The heat from the half-bridge GaN HEMTs propagates in the chip and leads to heating of the logic block and gate drivers. Heating of half-bridge GaN HEMTs leads to increased channel resistance and IC output current drop. Heating of the gate drivers reduces driving current, as a result, increases the switching time of the half-bridge GaN HEMTs. Heating of the logic block increases the rise and fall times of the generated control signals, which worsens the dynamic characteristics of the IC. A comparative analysis of heat propagation for IC dies based on GaN-on-SOI and GaN-on-Si heterostructures showed that GaN-on-SOI structure has a 40% greater junction-to-backside thermal resistivity compared to GaN-on-Si structure. In this case, the specific thermal resistance in the direction of heat propagation from the hotspot of the transistor to the backside of the die for the GaN-on-SOI structure is almost two orders of magnitude greater than in the direction of its propagation to the frontside of the chip. The results obtained were used for IC layout optimization. The rearrangement of GaN-on-SOI IC functional blocks, as well as to introduction of additional heat-spreading elements on the frontside of chip were carried out during the optimization.