In this work, a GaN-on-Si quasi-vertical Schottky diode was demonstrated on a locally grown n-GaN drift layer using Selective Area Growth (SAG). The diode achieved a current density of 2.5 kA/cm2, a specific on-resistance RON,sp of 1.9 mΩ cm2 despite the current crowding effect in quasi-vertical structures, and an on/off current ratio (Ion/Ioff) of 1010. Temperature-dependent current–voltage characteristics were measured in the range of 313–433 K to investigate the mechanisms of leakage conduction in the device. At near-zero bias, thermionic emission (TE) was found to dominate. By increasing up to 10 V, electrons gained enough energy to excite into trap states, leading to the dominance of Frenkel–Poole emission (FPE). For a higher voltage range (−10 V to −40 V), the increased electric field facilitated the hopping of electrons along the continuum threading dislocations in the “bulk” GaN layers, and thus, variable range hopping became the main mechanism for the whole temperature range. This work provides an in-depth insight into the leakage conduction transport on pseudo-vertical GaN-on-Si Schottky barrier diodes (SBDs) grown by localized epitaxy.