The performance of the AlGaN/GaN heterostructure based devices depends largely upon electrical behavior of Schottky contact which controls the current flowing through the channel. In this work, electrical behavior of Copper (Cu) Schottky diodes on Al0.25Ga0.75N/GaN heterostructures grown on Silicon have been investigated using temperature dependent current-voltage (I-V) and capacitance-voltage (C-V) techniques. An ideality factor (η) of 1.3 at room temperature (RT) signified that the forward current is dominated by thermionic emission process for current flow in the Schottky diode. The strong polarization field effects with in the barrier layer of the strained AlGaN/GaN heterostructure were considered for evaluating the barrier height using C-V measurements. The barrier height from such analysis was found to be 1.66 eV at RT which is significantly higher than theoretically predicted barrier height for Cu/AlGaN/GaN Schottky diodes. This observation of high barrier height is attributed to the presence of an ultra-thin Cu2O layer between Cu and AlGaN layer as revealed from scanning transmission electron microscopy. The temperature dependence of the barrier height suggests inhomogeneous nature of the Cu/AlGaN/GaN interface with different level of barrier inhomogeneities in different temperature ranges. Further, frequency-dependent C-V measurements were used to electrically characterize surface traps at Cu/AlGaN/GaN interface. Present study highlights the potential of Cu as a Schottky contact on AlGaN/GaN heterostructures for achieving high barrier height which is of utmost importance in GaN based device technology.