We have investigated the size-effect of the nano-Schottky diodes on the electrical transport properties and the temperature-dependent current transport mechanism in a metal-semiconductor nanowire junction (a Ti/GaN nano-Schottky diode) using current-voltage characterization in the range of 300-423 K. We found that the modified mean Schottky barrier height (SBH) was approximately 0.7 eV with a standard deviation of approximately 0.14 V using a Gaussian distribution model of the barrier heights. The slightly high value of the modified mean SBH (approximately 0.11 eV) compared to the results from the thin-film based Ti/GaN Schottky diodes could be due to an additional oxide layer at the interface between the Ti and GaN nanowires. Moreover, we found that the abnormal behavior of the barrier heights and the ideality factors in a Ti/GaN nano-Schottky diode at a temperature below 423 K could be explained by a combination of the enhancement of the tunneling current and a model with a Gaussian distribution of the barrier heights.