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The evolution of defect structure occurring during the cooling of Tellurium-rich CdTe is studied theoretically and experimentally. Classical nucleation theory is applied to comprehend the precipitation of excess Te and a formation of Te precipitates both in pure lattice and on extended defects is taken into account. Numerical simulations demonstrate significant effect of the cooling process on the room temperature precipitate magnitude and density. Theoretical results are compared with high temperature in-situ measurements of Te-rich CdTe:In. It is shown that the cooling rate significantly affects the temperature dependence of the conductivity. Characteristic temperatures, at which excess Te precipitates, are identified as apparent bows in measured dependencies. Optimum annealing-cooling treatment to obtain detector grade CdTe is suggested.