The intensification of the metallurgical manufacture, growing risk of damage lining steel casting ladles and isolation during fusion and flood of the metal, the compelled idle time of manufacture and significant cost of liquidation of emergencies, compels manufacturers of metallurgical production, to find ways of decrease in risk of possible occurrence of similar situations. One of ways of the decision of the given problems in metallurgical branch is introduction of the continuous or periodic control to process of manufacture, devices and systems of a condition lining domain, martin and electrosteel-smelting furnaces, and also stil casting ladles of various purpose. Researches of technological processes swimming trunks and flood of steel shows, that as a result of prolongation of service life lining ladles, due to a unreasonable conclusion of ladles from the operation, connected to visual survey so for example conducting metallurgical company " British Steel Corporation " saves about 340 thousand pounds sterling one year on one steelmaking manufacture. The control of a bricklaying lining one furnace for manufacture of a glass saves 250 thousand pounds sterling one year. The received result achieve due to use of monitoring systems of a temperature mode lining while in service and forms the basis for prolongation of term of its service. Application new systems, substantially, allows to expand opportunities of monitoring procedure and the analysis of the thermal phenomena proceeding in high-temperature melting furnaces, and testifies to an opportunity of creation of system of continuous monitoring their technical condition. The decision of the given task will allow to prolong term of operation of the furnace, practically to exclude risk of damage lining in result ïðîãàðà and to reach significant economic benefit. In my work mathematical methods of definition of a field of temperatures in lining a blast furnace on known temperatures in control points are considered. For this purpose the decision of a return task of heat conductivity which consists in changes on time of density of a thermal stream for surfaces bodies is necessary If on borders of a firm body dependence on time of a thermal stream or temperatures it is possible to define distribution of temperature in all a body is known. It is a so-called direct task. In many cases at the analysis of dynamic processes of heat exchange the law of change of a thermal stream or temperatures of a surface should be determined according to measurements of temperature in one or several internal points of a firm body. It is a return task. Within the framework of work carrying out of experiment by definition of a thermal field in a sample heated up with the face side is planned.