We identically prepared Cu-nMoSe2 (a-plane) and Cu-nMoSe2 (c-plane) Schottky barrier diodes (SBDs) on the same n-type MoSe2 single crystal. The effective Schottky barrier heights (SBHs) and ideality factors were obtained from the current-voltage-temperature (I—V—T) characteristics. The barrier height and ideality factor, estimated from the conventional thermionic emission model by assuming a Gaussian barrier distribution, are highly dependent on temperature. A notable deviation from the theoretical Richardson constant value is also observed in the conventional Richardson plot. The decrease in the experimental barrier height ΦB0 and an increase in the ideality factor n with a decrease in temperature have been explained on the basis of barrier height inhomogeneities at the metal-semiconductor interface. It is proven that the presence of a distribution of barrier heights is responsible for the apparent decrease of the zero bias barrier height. The voltage dependence of the standard deviation causes the increase of the ideality factor at low temperatures. The value of the Richardson constant obtained without considering the inhomogeneous barrier heights is much closer than the theoretical value. The Cu-nMoSe2 (a-plane) Schottky diode shows better results in comparison with the nMoSe2 (c-plane) Schottky diode.