We present a detailed model of the static and dynamic gate leakage current in lateral β-Ga2O3 MOSFETs with an Al2O3 gate insulator, covering a wide temperature range. We demonstrate that (i) in the DC regime, current originates from Poole–Frenkel conduction (PFC) in forward bias at high-temperature, while (ii) at low temperature the conduction is dominated by Fowler–Nordheim tunneling. Furthermore, (iii) we modeled the gate current transient during a constant gate stress as effect of electron trapping in deep levels located in the oxide that inhibits the PF conduction mechanism. This hypothesis was supported by a TCAD model that accurately reproduces the experimental results.