In a sealed electromagnetic relay, the change in the surface roughness mainly depends on the collision wear between the contact and the moving reed and the ablation effect of the arc on the contact surface based on the strong correlation between the contact resistance and the surface roughness of the Ag-Mg-Ni contact. With a change in contact resistance, the contact temperature increase in a hermetically sealed electromagnetic relay (HSER) is greatly affected. Under extreme overload conditions, the contact surface is severely ablated by the arc, and the roughness increases rapidly with the number of cycles, which greatly affects the contact resistance of the contact surface and the reliability of the relay. A thermal model of a relay contact system based on the surface roughness of Ag-Mg-Ni contacts was established in this paper by analyzing the effect of an arc on the surface roughness of Ag-Mg-Ni contacts under heavy overload conditions. The arc image of the Ag-Mg-Ni contact was recorded using a double-axis arc photographing platform, and the moving track of the arc center under overload conditions was drawn. This paper explored the patterns of arc center movement on the contact surface and the effects of the arc on the surface roughness of the contacts by analyzing the probabilities of the arc center appearing in various locations. A mathematical model correlating the number of contact cycles with contact resistance was established. Subsequently, a finite element simulation model for the equivalent heat source of the contact was developed. The theoretical model error was less than 10%. The accuracy of the equivalent heat source model was verified by comparing the measured data with the simulation results.