At this time the problem of monitoring the state of the contact wire is relevant. The condition of the contact wire is estimated by the values of mechanical and electrical wear, while the thermal wear of the contact wire is not determined. The paper considers the methodology for assessing the condition of the contact wire of electrified railways by the value of thermal softening. The presented methodology is based on the criterial approach. The criteria for softening the material of the wire and the transition of the material to the liquid state are introduced. By comparing the amount of heat entering the wire in the event of an electric arc, with these criteria, the contact wire is diagnosed in terms of thermal wear. Calculations have been made using the proposed methodology which makes an assessment of a condition of a contact wire on thermal softening depending on the initial data received in the operating of source data. When the calculation results are combined into databases, it is possible to estimate the residual life of the contact wire.