## 1 Introduction  
As the demand for mineral resources increases and mining intensities escalate, mines are progressively advancing into deeper extraction phases [1; 2; 3], and as mining depth increases, the temperature of the rock gradually rises. Geothermal heat in mines significantly impacts the safe operation of equipment, production efficiency, worker health, and labor productivity [4; 5; 6]. The cooling ventilation that follows underground roadway excavation induces a coupling between the temperature field of the mining area and the rock stress field, thereby altering the thermal and mechanical properties of rocks. This results in changes in the stress field surrounding the underground roadway, leading to the formation of fractured, plastic, and elastic zones [7]. According to research by [PERSON] et al. [8] under the combined effects of temperature and mechanical force, the rock failure process is linked to energy changes; heat conduction and the energy dissipation from plastic deformation of rocks can lead to instability and failure when reaching a critical maximum value. Moreover, modern rock constitutive relationship theory and the heat conduction equation play significant rolesin the issues of the thermal-mechanical coupling of rocks [9]. [PERSON] et al. [10] have compared coupled and uncoupled research methods, examining the relationships among temperature, stress, and strain fields in mining areas. In addressing a mine's thermal hazard, the study of rock thermal conductivity is foundational. Utilizing numerical simulation methods, [PERSON] [11] analyzed the variations in the rock temperature field under multi-field coupling conditions, while [PERSON] et al. [12] studied the effects of ventilation timing on the rock temperature field. [PERSON] [13] investigated the impact of seepage fields on rock temperature distribution, finding that low seepage speeds have minimal impact on rock temperatures. [PERSON] [14] developed computational software (Visual Basic 6.0, Aess2000) for the thermal and humid environment in underground roadways based on finite difference methods. [PERSON] et al. [15] researched the impact of various factors on rock heat transfer coefficients, identifying ventilation time as a critical factor. [PERSON] [16] through establishing a heat exchange model, analyzed the heat interaction between rock and ventilation and the effect of related parameters on the airstream temperature. [PERSON] et al. [17] by solving the temperature distribution function of underground roadway rocks, established theoretical formulas for the unstable heat transfer coefficient. [PERSON] [18] proposed an analytical solution coupling transient heat conduction in rock with the quasi-steady-state heat transfer process inside the mine. [PERSON] [19] developed a three-dimensional radial heat transfer model and used on-site temperature monitoring data to analyze complex boundary conditions on the roadway surface, studying the effects of convection heat transfer coefficients and insulation layer thickness on the lining temperature. [PERSON] [20] proposed a simplified one-dimensional heat transfer calculation method based on a surface heat source. Common methods used in gas-solid heat transfer research include empirical formulas, finite difference techniques, and numerical simulations; however, these often fail to consider the changes in rock thermal conductivity, thermal diffusivity, and specific heat capacity under high temperatures. This paper focuses on an underground roadway at depths of \(-930\) m and \(-945\) m in the Xishan mining area of Shandong Gold Sandsandao as the research subjects. It derives a differential equation for non-steady-state heat conduction applicable to the surrounding rock of metal mines, analyzes the characteristics and influencing factors of the thermal regulation zone expansion in deep surrounding rocks, and proposes a cloud monitoring system for the thermal field of deep mine rock.