The edge-defined film-fed growth (EFG) is a promising method to grow large beta-Ga2O3 crystal. The thermal field in the EFG system should be designed to provide proper conditions for growing large-size and high-quality crystals. 2D calculation of the meniscus shape and 3D global simulations are carried out to investigate and design the thermal fields in an EFG system for the growth of beta-Ga2O3 ribbon crystals. Effects of the induction coil position on the thermal field before seeding are firstly studied. Results indicate that it is difficult to improve all features of the thermal field just by changing the coil position. An improved design of adding a crucible cover is then proposed and investigated. It turns out that the crucible cover is a feasible design to improve the thermal field for the EFG growth of beta-Ga2O3 ribbon crystals comprehensively. The studies are expected to provide essential knowledge for further design and optimization of the EFG system.