We investigated the behavior of the forward bias current-voltage-temperature (I-V-T) characteristics of inhomogeneous (Ni/Au)-Al0.3Ga0.7N/AlN/GaN heterostructures in the temperature range of 295-415 K. The experimental results show that all forward bias semilogarithmic I-V curves for the different temperatures have a nearly common cross point at a certain bias voltage, even with finite series resistance. At this cross point, the sample current is temperature independent. We also found that the values of series resistance (R-s) that were obtained from Cheung's method are strongly dependent on temperature and the values abnormally increased with increasing temperature. Moreover, the ideality factor (n), zero-bias barrier height (Phi(B0)) obtained from I-V curves, and R-s were found to be strongly temperature dependent and while Phi(B0) increases, n decreases with increasing temperature. Such behavior of Phi(B0) and n is attributed to Schottky barrier inhomogeneities by assuming a Gaussian distribution (GD) of the barrier heights (BHs) at the metal/semiconductor interface. We attempted to draw a Phi(B0) versus q/2kT plot in order to obtain evidence of the GD of BHs, and the values of (Phi) over bar (B0)=1.63 eV and sigma(0)=0.217 V for the mean barrier height and standard deviation at a zero bias, respectively, were obtained from this plot. Therefore, a modified ln(I-0/T-2)-q(2)sigma(2)(0)/2(kT)(2) versus q/kT plot gives Phi(B0) and Richardson constant A(*) as 1.64 eV and 34.25 A/cm(2) K-2, respectively, without using the temperature coefficient of the barrier height. The Richardson constant value of 34.25 A/cm(2) K-2 is very close to the theoretical value of 33.74 A/cm(2) K-2 for undoped Al0,3Ga0,7N. Therefore, it has been concluded that the temperature dependence of the forward I-V characteristics of the (Ni/Au)-Al0.3Ga0.7/AlN/GaN heterostructures can be successfully explained based on the thermionic emission mechanism with the GD of BHs.