Temperature T dependences of the current-voltage (I-V) characteristics of Ni and Pt/n-GaN Schottky contacts were measured in detail, and the results were analyzed from various viewpoints. Large deviations from the thermionic emission transport were observed in the I-V-T behavior with anomalously large reverse leakage currents. Forward characteristics could be fitted into the classical thermionic-field emission (TFE)/field emission (FE) model. However, an unusually high doping density had to be assumed, and the reverse characteristics were far away from measured data. A new thin surface barrier (TSB) model was proposed in which the width of the Schottky barrier is reduced due to the presence of unintentional surface donors. Analysis of TFE/TE process through the TSB region has led to sets of I-V-T curves that reproduce almost perfectly the observed forward and reverse I-V-T behavior with correct orders of magnitude, of currents. Deep donors related to nitrogen vacancy are suggested to be the origin of surface donors producing TSBs.