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This paper describes a method for determining the heat conductivity coefficient based on solving the quasi-inverse multivariate problem of the heat conductivity in cylinder, which is heated with the radiant flux from the face and radiates freely with the constant temperature from all sides into the medium. A sample radiant heating can be carried out by different methods, e.g. by means of optical furnace, laser or high temperature furnace. To determine the heat conductivity coefficient and the error estimation with the radiation flux the mathematical simulation was carried out. At first the direct problem of heat conductivity was solved. The calculation resulted in determination of the total heat flow departing from the low surface of the sample. Accuracy assurance of solving is the convergence of heat balance. Then the inverse problem was solved by means of which the heat conductivity coefficient was determined by the known density of incoming heat flow and the total heat flow.