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The results of study of a tree inception and growth in polar dielectrics with amorphous and cross-linked structure in the divergent field under AC voltage in visible and IR spectra are represented in this paper. It is determined that the treeing inception and growth processes in polar dielectrics are accompanied by step-wise changes of the dielectric surface temperature. These temperature changes correspond to the induction stage, the growth stage and pre-breakdown stage. Transition from previous stage to next one is accompanied by the increase in the local temperature difference on the dielectric surface by a factor of 1.5-2.0. A new model of the individual diagnostics of the main characteristics of the treeing process and the remaining lifetime for polar dielectrics was suggested on the basis of temporal-temperature analysis of the dielectric aging process.