## 7 Conclusions  
To address the issue of thermal hazard in deep metal mines, a non-steady-state heat conduction differential equation suitable for the surrounding rock of metal mines underground was derived based on the thermal property changes of rocks under high temperature. The characteristics of the thermal circle for rock adjustment were obtained, and a temperature field cloud monitoring system based on high-precision temperature acquisition equipment was proposed. The main conclusions are as follows:  
1. Based on the principles of Taylor series expansion and thermal equilibrium, a differential equation for non-steady-state heat conduction suitable for the surrounding rock of metal mines was derived. By substituting the thermal-physical parameters of various rock groups into the finite difference equation for calculation, the expansion of the radius of the thermal circle in the surrounding rock is mainly influenced by temperature and rock type, leading to different ranges of variation.
2. With the engineering environment at depths of 700 to 1200 m in Sanshandao Gold Mine as the background, the radius and temperature distribution of the thermal circle in the surrounding rock are influenced by many factors. As the original rock temperature increases, the thermal circle radius gradually increases, while with the increase in ventilation distance, the thermal circle radius gradually decreases. The variation in the original air temperature has a significant impact on the temperature distribution in the roadway surrounding rock. As the ventilation temperature decreases, the thermal circle radius gradually increases. However, the variation in the thermal circle radius due to changes in the length of the roadway affected by the airflow is relatively small. With the increase in ventilation speed, the temperature distribution in the surrounding rock at different locations in the roadway tends to be more uniform. The roadway wall has the largest temperature difference, and with the increase in ventilation speed, the thermal circle radius gradually increases, with less influence from the ventilation distance. The distribution of the surrounding rock temperature field in the roadway after 180 days of ventilation was calculated. It was found that the thermal circle radius is simultaneously influenced by thermal-physical parameters and the original ground temperature.
3. During the temperature monitoring period, the highest temperatures of the surrounding rock at the \(-930\) m and \(-945\) m measurement points reached \(34.5\)\({}^{\circ}\)C and \(36.7\)\({}^{\circ}\)C, respectively. By calibrating the model using the actual measured temperatures, the calibrated model indicates that the rock temperature begins to stabilize at a depth of \(28.11\) m.  
Conceptualization, T.L.; writing--original draft, T.L., H.S., Z.F. and Q.F.; writing--review and editing, P.X. and H.J.; project administration, H.J.; Investigation, T.L., P.X., H.S., Z.F. and Q.F. All authors have read and agreed to the published version of the manuscript.  
This work was funded by National Key Research and Development Program of China, 2023 YFC29074001, 2023 YFC29074003.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
The author [PERSON] is currently studying the preamble for a PhD in Civil Engineering in Civil and Resource Engineering at the University of Science and Technology Beijing. The remaining authors state that the study was conducted without any business or financial relationships, which could be interpreted as a potential conflict of interest.