Sulfur hexafluoride (SF6) has been widely employed in the power industry as an arc quenching medium. However, its extremely high global warming potential has led to urgent efforts to reduce or replace its use. Identifying eco-friendly substitutes is particularly challenging because candidate gases are often complex mixtures that must operate reliably under diverse conditions. Traditional evaluation of arc quenching performance relies on magnetohydrodynamic (MHD) models, which are computationally intensive and must be recalculated whenever the operating parameters change. To overcome these limitations, we propose Arc-DeepONet, a deep operator network framework designed to solve the time-dependent Elenbaas–Heller equations and to predict arc quenching performance with significantly reduced computational cost compared to conventional two- or three-dimensional MHD arc models. Arc-DeepONet learns the nonlinear mapping between input conditions (e.g. boundary conditions, gas composition) and arc temperature fields, from which arc conductance and two key evaluation metrics (i.e. thermal recovery rate and pre-dielectric recovery rate) are derived. The method is validated on SF6 and several candidate alternative gases, including C4F7N, CO2, and C4F7N–CO2 mixtures. Results show that Arc-DeepONet can accurately reproduce the arc decay process with relative L2 errors below 10−2, while reducing computation time from hours to seconds. Moreover, the predicted arc-quenching metrics reliably quantify the performance of different gases, demonstrating the potential of Arc-DeepONet as an efficient tool for rapid screening and optimization of eco-friendly SF6 alternatives.