Some current-voltage characteristics of GaAs MESFET at elevated temperatures have been measured and the existence of zero temperature coefficient (ZTC) points in the drain current of DFETs and EFETs are presented. At these points of operation, with a specific value of gate bias, the device drain current characteristics are stable in temperature. The ZTC point for the saturation region of operation is presented for both types of devices, whereas for the linear region of operation the ZTC point is reached only with DFET. The existence of the ZTC point is shown to depend critically on the flow of leakage currents. The ZTC points are analysed with an analytical model that is capable of estimating the corresponding drain current and gate bias values. In addition, an analytical model for the threshold voltage and transconductance parameter is discussed by starting from device physical and geometrical parameters for finding the ZTC point. The analytically solved results are shown to correspond closely to the experimental results.