Background. The relevance of this work is due to the need to improve the lowefficiency traditional methods of monitoring emergency situations at industrial facilities. In the course of the study, a case of an electric arc in the brush traverse of an electric generator is considered, which led to a violation of the thermal balance and an emergency catastrophic increase in temperature, not timely detected by the existing tolerance control system. Materials and methods. According to the method of data sliding sample on the experimental trend of generator temperature growth, an assessment of the parameters of the heat balance equation was carried out, which showed that the violation of the thermal balance led to the occurrence of a type A1 disaster. Results. It was assumed that the catastrophic increase in temperature was caused by the reflection of part of the thermal energy by the generator housing into this housing. Assuming that the amount of energy emitted by the housing obeys the Stefan-Boltzmann law, a heat balance equation was obtained taking into account the internal reflection of thermal energy, which showed that the occurrence of elementary Arnold disasters of types A1-A4 is theoretically possible. A forecasting method is proposed, using which the disaster detection time is reduced by 200 minutes, compared to the time of emergency detection by a traditional monitoring system. Conclusions. It is proven that the process of accident development in an electric generator is caused by excessive heat inflow and the presence of a heat-reflecting screen (generator housing). The presence of such screen disrupts the natural process of heat exchange and if we assume that the amount of energy emitted by the screen will obey the Stefan-Boltzmann law, then in accordance with the classification of disasters, the occurrence of elementary disasters of the type is theoretically possible: A0 - non-singular point; A1 - local extremum (stable minimum or unstable maximum); A2 - fold; A3 - assembly. Parametric identification of the nonlinear heat balance equation was performed using the sliding sample method. The maximum error in calculating the emergency mode temperature using this equation does not exceed 30 C. With sufficient accuracy for practice, the heat balance equation corresponds to the classification of elementary disasters by Thom, which can lead to the occurrence of a type A1 disaster.