We present a method to determine the average device channel temperature of AlGaN/GaN metal-oxide-semiconductor heterostructure field effect transistors (MOSHFETs) in the time domain under continuous wave (CW) and periodic-pulsed RF (radiation frequency) operational conditions. The temporal profiles of microwave output power densities of GaN MOSHFETs were measured at 2 GHz under such conditions and used for determination of the average channel temperature. The measurement technique in this work is also being utilized to determine the thermal time constant of the devices. Analytical temporal solutions of temperature profile in MOSHFETs are provided to support the method. The analytical solutions can also apply to generic field effect transistors (FETs) with an arbitrary form of time-dependent heat input at the top surface of the wafer. It is found that the average channel temperature of GaN MOSHFETs on a 300 pm sapphire substrate with the output power of 10 W/mm can be over 400 degrees C in the CW mode while the average channel temperature of GaN MOSHFETs on a SiC substrate with the same thickness only reaches 50 degrees C under the same condition. The highest average channel temperature in a pulsed RIF mode will vary with respect to the duty cycle of the pulse and type of the substrate. (C) 2008 Elsevier Ltd. All rights reserved.