Multi-channel GaN HEMTs enhance the overall device performance by vertically stacking multiple AlGaN/GaN heterojunctions. This structure increases the total two-dimensional electron gas (2DEG) concentration while maintaining high mobility in each channel. However, it also introduces complex self-heating challenges. Although current sharing among multiple channels reduces the average heat flux per channel, the dense vertical stacking leads to significant inter-channel thermal coupling. This coupling particularly degrades heat dissipation in the middle channels, resulting in severe non-uniform temperature distribution. The gate-drain region sustains both high current density and high electric field, causing concentrated heat flux distribution and further aggravating self-heating effects. To address these issues, this work develops a bidirectional electro-thermal coupling model for multi-channel GaN HEMTs. The model self-consistently solves the drift-diffusion equations and the Fourier heat conduction equation. Bidirectional coupling is achieved by incorporating the temperature dependence of carrier mobility. This approach accurately characterizes the electro-thermal distribution of the device. Simulation results reveal significant vertical thermal coupling between adjacent channels. The middle channel exhibits the most severe temperature rise, with its temperature approximately 15-20 K higher than that of edge channels under typical operating conditions. Moreover, the current density degradation caused by self-heating in the hottest channel reaches a non-negligible level, fully demonstrating the necessity of coupled simulation. Based on the advantages of field plates in optimizing electric field distribution and improving breakdown voltage, this study further explores their feasibility in suppressing self-heating by modulating the channel electric field. The effects of four different gate-drain field plate structures on electric field and heat flux distribution are systematically evaluated. Results show that the slanted field plate is the most effective configuration. Its underlying mechanism is transforming the single large potential drop concentrated at the gate edge into multiple gradual steps along the channel. This smoothes the electric field distribution and significantly reduces the peak heat flux density. Through parametric optimization, an optimal configuration with a 6° slant angle and 1.2 μm length is identified. Compared to the structure without a field plate, this design reduces the peak electric field and peak heat flux density by approximately 75%. The maximum channel temperature decreases from 472.8 K to 461.9 K, a reduction of about 6%, while the device's electrical performance remains largely unaffected. This study provides critical insights into the unique electro-thermal coupling mechanisms in multi-channel GaN HEMTs. It also demonstrates that optimally designed slanted field plates offer an effective approach for enhancing the thermal reliability of high-performance GaN power devices.