In [1, 2] based on modern concepts the results of many years of research on the development and implementation of a heat control system for refractory lining of a blast furnace hearth are presented. A system for monitoring the condition of the refractory lining of a blast furnace hearth is proposed, designed to prevent emergency situations. The duration of the blast furnace campaign, that is, the time from one major repair to another, ranges from 5 to 20 years. One of the reasons that can significantly shorten the campaign period is the breakthrough of liquid cast iron through the lining of the lower part of the blast furnace (hearth). The analysis of existing methods for monitoring the condition of the refractory lining of a blast furnace hearth and extending the duration of its campaign in the world is presented. A mathematical description, algorithm, and computer program for calculating two-dimensional temperature fields in any vertical and horizontal section of the blast furnace hearth lining have been developed. The calculation is carried out by solving the equations of thermal conductivity using the readings of a large number of temperature sensors (up to 700) mounted in the lining of the furnace between the refractory blocks. The calculation algorithm has been improved in terms of taking into account the complex profile of the lower part of the blast furnace using the counting theorem. A system for collecting, processing and transmitting information from temperature sensors to the program database is used. Continuous monitoring of temperature changes at each point allows you to determine the remaining thickness of the refractory lining or the appearance of a scull and warn the furnace staff about the beginning of the lining heat. The developed program interface allows the furnace master to use many additional monitoring functions, in particular, the history of sensor readings, remaining wall thickness, etc. The monitoring systems for the refractory lining of the blast furnace hearth are installed at five blast furnaces of metallurgical plants in China and six blast furnaces in Russia.