The increasing demand for tightly integrated gallium nitride high electron mobility transistors into electronics systems requires accurate thermal evaluation. While these devices exhibit favorable electrical characteristics, the performance and reliability suffer from elevated operating temperatures. Localized device self-heating, with peak channel and die level heat fluxes on the order of 1 MW cm-2 and 1 kW cm-2 respectively, presents a need for thermal management that is reliant on accurate channel temperature predictions. In this publication, a high-fidelity multiphysics modeling approach employing one-way electrothermal coupling is validated against experimental results from Raman thermometry of a sixty-finger GaN HEMT power amplifier under a set of DC-bias conditions. A survey of commonly assumed reduced order approximations, in the form of numerical and analytical models, are systematically evaluated with comparisons to the peak channel temperature rise of the coupled multiphysics model. Recommendations of modeling assumptions are made relating to heat generation, material properties, and composite layer discretization for numerical and analytical models. The importance of electrothermal coupling is emphasized given the structural and bias condition effect on the heat generation profile. Discretization of the composite layers, with temperature dependent thermal properties that are physically representative, are also recommended.