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Thermal shocks on line insulators produced by arcs, which may be intentionally repeated due to reclosing, or randomly caused by arc-backs etc., are investigated. A quantitative analysis of this phenomenon has been developed. The total arc power at the arc-insulation interface required for the analysis has been estimated experimentally for currents up to 850 A. Arc power appears to be proportional to current. The approach adopted is identical for both fragile and elastic materials since the temperature is chosen to be at threshold. The consequences of surface arcing for a new insulator material can be predicted approximately, using the relationships presented in the paper. The heaviest thermal shock appears to be proportional to the square root of the number of arcings. A doubled reclosing can contribute between 25 and 50% increase in the thermal shock compared to that of a single arc. With moderate arcs, the effect of material properties on the temperature rise for single or multiple shocks is similar. It is recommended that the thermal shock due to repeated arc-back be calculated as an equivalent single arc with the time equal to the sum of all individual times.