In this work, the electrical properties of Ni/GaN Schottky contacts formed on high-temperature annealed (1100–1200 °C) GaN surfaces were studied. Although the morphology of the GaN surface was not changing after annealing, a worsening of the electrical behavior of the Schottky contact occurred, with a reduction in the barrier height and an increase in the leakage current. Moreover, a different temperature dependence of the reverse electrical characteristics of the Schottky diodes was observed. In particular, for the sample annealed at 1150 °C for 5 min, one-dimensional variable-range-hopping conduction was one of the dominant carrier transport mechanisms. The presence of a high density of interface states was indicated as a possible reason of this electrical behavior.