## 5 Conclusions  
In this study, a two-dimensional heat transfer model of the roadway-surrounding rock is formulated, and the temporal and spatial evolution of the temperature field of the roadway-surrounding rock is scrutinized. Utilizing the Gauss-Newton method, the temporal and spatial coupling characteristics of the temperature field of the roadway-surrounding rock and the impact of thermal conductivity on it are examined. The key conclusions are outlined below:  
1. The evolution law of the temperature field of the roadway-surrounding rock in an unventilated state is examined. The findings reveal that in the spatial dimension, the dimensionless temperature of the surrounding rock gradually increases, and the rate of temperature rise diminishes until it reaches the initial temperature of the original rock during the radial extension of the surrounding rock into the deep. In the time dimension, as the ventilation time increases, the infinite temperature of the surrounding rock gradually decreases, and the cooling rate progressively diminishes until it stabilizes at a fixed value.
2. The space-time coupling characteristics of the temperature field of the roadway-surrounding rock are examined. The findings demonstrate that the function \(\Theta=\frac{-\exp\left(A\times R^{\text{B}}\right)}{\Omega\times R\times R^{ \text{O}}+\exp\left(\mathbb{S}\times R^{\text{O}}\right)}+1\) can represent the coupling characteristics of the surrounding rock temperature field. In the time dimension, as the ventilation time increases, the fitting degree of the characteristic curve gradually improves. The characteristic curve moves downward as a whole, leading to a gradual decrease in dimensionless temperature and a reduction in the temperature drop rate. In the spatial dimension, with the increase in the dimensionless radius, the fitting degree of the characteristic curve decreases in the deep part. The characteristic curve moves upward as a whole, resulting in a gradual increase in dimensionless temperature while the temperature rise rate gradually decreases.
3. This study investigates the impact of thermal conductivity on the temporal and spatial coupling characteristics of the temperature field in the surrounding rock of roadways. The findings indicate that a higher thermal conductivity corresponds to a higher fitting degree of the coupling characteristic function of the surrounding rock. Moreover, under the same ventilation time, larger thermal conductivity results in a smaller wall cooling range, a greater internal temperature drop rate of the surrounding rock, and a larger range of disturbed surrounding rock.  
Conceptualization, J.Z. and Y.Z.; methodology, J.Z.; validation, P.S. and Y.L.; investigation, Y.L.; writing--original draft preparation, J.Z.; writing--review and editing, Y.Z.; visualization, P.S.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (52074266).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare that they have no conflicts of interest.