Aluminum gallium nitride (AlGaN)/gallium nitride (GaN) high electron mobility transistor (HEMT) has shown great potential and superiority over other devices in high power and high speed-based systems [1-4]. Recently, a novel AlGaN/GaN HEMT structure named triple material gate (TMG) HEMT has been proposed in [5] in which the gate contact is composed of three metals with different work functions. TMG HEMT ensures high carrier velocity and better suppression of short channel effects. In this work, a two-dimensional electro-thermal model has been developed to investigate the joule heating effect in TMG AlGaN/GaN HEMT using the software COMSOL [6]. The current continuity and heat transport equations are solved self-consistently to obtain the temperature distribution profile in various layers of the device. Thermal efficiency of TMG HEMT is compared with dual material gate and single material gate HEMT. It has been found that, besides providing better current carrying capability, TMG HEMT shows optimum thermal performance. Moreover, the variation of peak temperature in the channel with drain and gate voltages is analyzed to study the bias voltage dependence of the device temperature rise. Effects of several device parameters like total channel length, spontaneous and piezoelectric polarization induced charges and ratio of lengths of control and screen gates, on the thermal performance have also been explored. Simulations are carried out for the device lying on different substrate materials (Sapphire, GaN, Si and SiC) with varying thermal conductivity to demonstrate their performance in heat removal capacity. This simulation model can serve as a very useful tool to comprehend the thermal behavior of the device for high power and high frequency applications.