Static induction transistors (SITs) are short channel FET structures which are suitable for high power, high frequency and high temperature applications. GaN has particularly favorable properties for SIT operation. However, such a device has not yet been fabricated. In this paper we report simulation studies on GaN static induction transistors over a range of device structures and operating conditions. The transistor was modeled with coupled drift-diffusion and heat-flow equations. We found that the performance of the device depends sensitively on the thermal boundary conditions, as self-heating effects limit the maximum voltage swing.