High power Gallium Nitride (GaN) based field effect transistors are used in many high power applications from RADARs to communications. These devices dissipate a large amount of power and sustain high electric fields during operation. High power dissipation occurs in the form of heat generation through Joule heating which also results in localized hot spot formation that induces thermal stresses. In addition, because GaN is strongly piezoelectric, high electric fields result in large inverse piezoelectric stresses. Combined with residual stresses due to growth conditions, these effects are believed to lead to device degradation and reliability issues. This work focuses on studying these effects in detail through modeling of Heterostructure Field Effect Transistors (HFETs) and metal oxide semiconductor hetero-structure field effect transistor (MOSHFETs) under various operational conditions. The goal is to develop a thorough understanding of device operation in order to better predict device failure and eventually aid in device design through modeling. The first portion of this work covers the development of a continuum scale model which couples temperature and thermal stress to find peak temperatures and stresses in the device. The second portion of this work focuses on development of a micro-scale model which captures phonon-interactions at the device scale and can resolve local perturbations in phonon population due to electron-phonon interactions combined with ballistic transport. This portion also includes development of phonon relaxation times for GaN. The model provides a framework to understand the ballistic diffusive phonon transport near the hotspot in GaN transistors which leads to thermally related degradation in these devices.