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Electrode replacement is an effective method to extend the useful lifetime of the spark gap switch with graphite electrodes. In order to perform electrode replacement, suppressing temperature rise and preventing static welding/erosion should be considered for the static electrical contact interface between the electrode and the holder. In this paper, a mathematical model of contact temperature rise is proposed based on the Holm model and heat-conduction equations. This mathematical model can quantitatively prove that some material properties of the metal holder and some mechanical characteristics of the spark gap switch are key parameters affecting temperature rise. Material properties of the metal holder include thermal conductivity, specific heat, density, electrical resistivity, elasticity modulus, and the Poisson ratio. Mechanical characteristics of the spark gap switch include contact radius/area, contact pressure, and contact surface roughness. Optimum configuration of these key parameters reduces temperature rise and prevents static welding/erosion.