As a newly emerged semiconductor, β-Ga₂O₃ has an ultra-wide bandgap (E_g) of 4.8 eV and corresponding empirical high electrical breakdown field (E_br) of 8 MV/cm as well as 300 cm²/V·s room temperature (RT) mobility (μ), which is identified as the next generation semiconductor to replace GaN and SiC. However, β-Ga₂O₃ field-effect transistors (FETs) on its native substrates suffer from severe self-heating effect due to its low thermal conductivity of 10~25 W/m·K. One approach to minimize self-heating effect is introducing β-Ga₂O₃ on insulator (GOOI) FET structure by replacing β-Ga₂O₃ native substrate with a higher κ and wider E_g substrate through wafer bonding technique. Here, we demonstrate that by utilizing a higher thermal conductivity sapphire substrate rather than SiO₂/Si substrate, the temperature rise above room temperature of β-Ga₂O₃ GOOI FET can be reduced by a factor of 3 and thereby the self-heating effect is significantly reduced. Both thermo-reflectance characterization and simulation verify that the thermal resistance on sapphire substrate is less than 1/3 of that on SiO₂/Si substrate. Therefore, maximum drain current density of 535 mA/mm is achieved on sapphire substrate, which is 70% higher than that on SiO₂/Si substrate, due to reduced self-heating. Integration of β-Ga₂O₃ channel on a higher thermal conductivity substrate opens a new route to address the low thermal conductivity issue of β-Ga₂O₃ for power electronics applications.