Our investigation explores the complex interplay between electromagnetic field and heat transfer during the fusion process of pure gold within an induction crucible furnace through a 2D-axisymmetric model. By constructing this model, we analyze the critical warm-up phase-a period marked by substantial power requirements and extended duration. This research seeks to illuminate how various geometrical and physical parameters influence the distribution of physical fields throughout the transient heating interval. Of particular interest is the path to achieving optimal melting conditions, given the intricate coupling between electromagnetic and thermal phenomena, both of which exhibit significant nonlinear characteristics. To address these challenges, we developed a computational framework based on finite volume discretization to numerically solve the governing equations of electromagnetic and heat conduction.