High quality, large-scale silica glass crucibles are strongly required for large-diameter silicon crystal production using the Czochralski process. Silica glass crucibles are usually produced from silica powder, which is fused at high temperature in an arc. In this study, we made a numerical analysis model taking account of the high temperature plasma jet induced by the arc between carbon electrodes, and measured the temperature variation of the fusing silica powder in a crucible-production process to verify the propriety of the analytical model. The calculated results were found to show good agreement with the actual temperature measurements. The arc furnace was found to have two different heating conditions that depend on the crucible positions. One is put under the control of high-temperature jet generated by the arc. The other is put under the control of radiation heat transfer near the electrodes. Our developed calculation model is expected to be of use in clasifying the optimum conditions for the fusing mechanism in the arc furnace.