The BeMgZnO/ZnO heterostructures are capable of producing sufficiently high sheet electron densities to allow field effect transistor operation near or at the LO phonon plasmon resonance frequency for minimal LO phonon lifetimes and high electron velocity. Schottky barriers are imperative for the implementation of the aforementioned devices. Therefore, we have undertaken fabrication and characterization of Ag Schottky barriers on Zn‐polar Be0.02Mg0.26ZnO/ZnO heterostructures, exhibiting the said two‐dimensional electron gas (2DEG), grown by molecular beam epitaxy. Ag Schottky barriers are characterized by current–voltage (I–V) measurements in the temperature range from 80 to 400 K. At room temperature, the highest barrier height of 1.07 eV and an ideality factor of 1.22 are achieved with a rectification ratio of about eight orders of magnitude. Richardson constants of 38 ± 22 and 29 ± 20 A cm−2 K−2 are found using modified Richardson plots from Schottky diodes fabricated on two different structures. These values are consistent with the theoretical estimate of 36 A cm−2 K−2 for Be0.02Mg0.26ZnO. The temperature variation of barrier heights and ideality factors, an aberration from pure thermionic behavior, has been explained with plausible spatial inhomogeneity of barrier height with three Gaussian distributions in the temperature ranges of 80–200, 220–280, and 300–400 K.