## 1 Introduction  
Coal is a major fossil energy resource and is extensively used worldwide [1]. The underground environment in underground mining is usually dark and damp. The mining environment contains flammable and explosive gases and dust. Therefore, underground coal mines must impose strict safety requirements on electrical equipment. In an explosive underground atmosphere containing gases and dust, the Coal Mine Flameproof Cable Box is used for connecting and branching power cables in AC power supply networks. Explosion-proof cable boxes are typically used in coal mines to ensure that the external explosive environment is protected from electrical sparks, combustion, and internal explosions [2]. However, closed structures do not dissipate heat efficiently. Prolonged overloading and short-circuiting can increase the temperature of internal connecting wires, terminals, and other components [3]. High temperatures caused by operating in fault mode are the main cause of explosion-proof cable box failures in coal mines. Furthermore, operating the box at high temperatures reduces mechanical strength, causes structural damage, and reduces insulation capability. Thus, production accidents such as phase-to-phase short circuits, electrical fires, and gas explosions are highly likely to occur [4, 5].  
The temperature characteristics of electrical equipment have been extensively investigated. For example, [PERSON] et al. established a cable and cable joint temperature computing model based on the multi-physics field. Using this model, they not only analyzed the effects of thermal conductivity, temperature, and wind speed on the temperature distribution characteristics of the cable but also studied the relationship between the current propagation speed and the cable temperature [6; 7; 8]. [PERSON] et al. developed a three-dimensional (3D) temperature field simulation model for electric motors to analyze the influence of the ambient temperature, wind velocity, and radiators on temperature fields; understand the relationship between temperature and silicon steel sheet losses; and develop a permanent magnet temperature evaluation method [9; 10; 11; 12]. By simulating and experimentally validating temperature rises of medium voltage switchgear used for power transmission and distribution, [PERSON] et al. proposed a novel temperature simulation method that can be implemented by adjusting heat transfer coefficients [13; 14]. [PERSON] et al. proposed a simplified computational fluid dynamics model to investigate the heat dissipating capacity of a transformer and the temperature distribution characteristics of windings in the transformer [15; 16; 17]. Existing research on temperature characteristics is focused on temperature distribution characteristics, the influence of environmental factors on temperature, the relationship of temperature and losses, and the development of a permanent magnet temperature evaluation method in normal operating conditions. Limited research has been conducted to address the failure of explosion-proof electrical equipment in coal mines. In this scenario, it is crucial to study the temperature characteristics of magnetic coupling-based explosion-proof cable boxes for coal mines, especially in the failure mode.