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The present article is devoted to the mathematical model development of a deciduous tree ignition by a cloud-to-ground lightning discharge. The physical and mathematical statement of the deciduous tree ignition problem using the large vessels approach is presented. The problem is considered in a flat statement in polar coordinates. The deciduous tree trunk warming up under the influence of the cloud-to-ground lightning discharge current has been researched. The thermal emission through the tree trunk during the discharge current passage is described by the Joule-Lenz law. The influence of large vessels moisture and its evaporation on a temperature field formation in the deciduous tree trunk is investigated. The possibility of the deciduous tree ignition caused by the cloud-to-ground lightning discharge is established.