The output characteristics of AlGaN/GaN semiconductor heterostructure field effect transistors are strongly dependent on the ambient temperature of the channel region due to relatively large variations in the electron drift velocity with temperature. A model to simulate the heat flow in AlGaN/GaN HFETs on sapphire and SiC substrates is presented. The nonlinearity of the problem arising from the temperature dependencies of the III-nitride and substrate thermal conductivities is examined through the technique of self-consistent boundary conditions. It is found that the use of the linearizing Kirchhoff transformation is a good approximation for these systems. Alternative approaches of heatsinking the devices from the top of the wafer are explored also.