## 3 Results and Discussion
### Variation Patterns of Temperature at Monitoring Points  
Figure 5 illustrates the temperature variations of monitoring points on lines G-G, E-E, and H-H and in the fracture over time under 80 \({}^{\circ}\)C heat source heating. Based on Figure 5, it is evident that during the heating process, the temperature of each monitoring point undergoes three primary stages: (1) a rapid heating stage (I), which takes a short time but has a large heating range and lasts for approximately 1 h; (2) a slow heating stage (II), which lasts for about 3 h and experiences a gradual transition from unsteady heat conduction to steady heat conduction; and (3) a temperature stabilization stage (III), the temperature is relatively stable in this stage, with the temperature essentially unchanged. Further observation of the curve reveals that the temperature from the monitoring points below the fracture (e.g., 3#, 23#, and 43#) compared to those above the fracture (e.g., 21#, 41#, and 61#) has dropped sharply. This indicates that the fracture has significantly impeded heat transfer in the granite. The temperature at monitoring points 12#, 32#, and 52# in the fracture is nearly the same as that of the points below the fracture, yet it significantly differs from the temperature of the points above it. Figure 5: Temperature variation curves of monitoring lines under 80 \({}^{\circ}\)C heat source heating: (**a**) line G-G; (**b**) line E-E; (**c**) line H-H; (**d**) in the fracture. The presence of the fracture significantly influences the temperature distribution in granite. To further study the steady temperature distribution characteristics around the fracture in granite, Figure 6 illustrates the curves of the steady temperature of the monitoring points on different monitoring lines around the fracture with the position of the monitoring points when heated for 540 min at different heat source temperatures. It can be seen from Figure 6 that inside of the granite, the monitoring line A-A is situated on the left side of the granite, and the monitoring line C-C is positioned on the upper part of the fracture. The steady temperature of the monitoring points along these two lines decreases nonlinearly as the \(d_{\text{h}}\) increases. Conversely, the monitoring line B-B is located on the right side of the granite, and the monitoring line D-D is situated on the lower part of the fracture. The steady temperature of the monitoring points on the two monitoring lines decreases linearly with the increase in the distance from the monitoring point to the heat source. A combination of Figures 5 and 6 shows that the presence of the fracture alters the distribution characteristics of the steady temperature within the granite. This is because in the lower area of the fracture, the heat transfer is primarily carried out by heat conduction, and the heat flow has not been significantly disturbed before reaching the fracture. The heat can be transferred to the lower wall of the fracture more uniformly, which still adheres to the one-dimensional linear heat conduction law [35]. In addition, as \(d_{\text{v}}\) increases, the degree of heat loss gradually increases, which leads to the trend of a linear decrease in  
Figure 6: The relationship between the steady temperature of the monitoring points and the distance from the heat source (\(T_{\text{h}}=80\) °C): (**a**) line A-A; (**b**) line B-B; (**c**) line C-C; (**d**) line D-D.  
the steady temperature. On the contrary, in the upper region of the fracture, heat transfer involves the combination of the fracture itself and the surrounding rock. A portion of the heat transfer needs to bypass the air fracture. Due to the influence of the fracture's geometry, the heat passing through the granite bypass path causes the heat flow's direction to deflect. In addition, another part of the heat transfer needs to be transferred through the fracture.