## 1 Introduction
Because more accurate experimental conditions can be applied and the temperature of rock can be measured more precisely in the laboratory, researchers have conducted a series of laboratory experiments to study the temperature effect of rock during the deformation and fracturing processes. Uniaxial compression [26], multiaxial compression and shear tests [27; 28] on rocks with different lithologies [29] proved that the infrared radiation of rocks would change under different stress conditions. In order to accurately grasp the characteristics of infrared radiation evolution, a variety of methods were used to process the infrared radiation data [30]. In addition to using the average temperature [31], a variety of parameters were also introduced to characterize the temperature evolution process and predict rock failure, for example, the temperature standard deviation index [32], characteristic roughness, entropy, and variance [33], continuous minimum infrared image temperature variance [34], instantaneous variance of infrared image sequence [35], infrared radiation b value [36], temperature concentration coefficient [37], and temperature variation coefficient [38]. On this basis, the influencing factors of infrared radiation are further studied. It is considered that the temperature change is related to the type of fracture [27], water in rock [39], volume strain [40], stress [41], and heat conduction effect [42]. In these studies, the temperature evolution can be captured and analyzed in conjunction with the stress-strain curves and macro-fractures; however, these studies are always based on the observation of the temperature change of the rock, with no detailed information including the stress and strain distribution, the micro-crack initiation and propagation, etc., known. Consequently, the mechanism of the temperature variation during the rock deformation and fracturing process is still not clear. In recent years, the development of numerical modeling has provided us with a new way of analyzing mechanical and thermal behaviors. [PERSON] et al. [43] carried out a series of numerical calculations on metal materials with a finite element numerical calculation of metal materials. In addition, the results show that elastic tension causes a temperature drop, while elastic compression causes the temperature to rise in the elastic stage. However, if the material is in the elastic-plastic deformation range, plastic tension, elastic compression, and plastic compression lead to an increase in the material temperature, while elastic tension leads to a decrease in the material temperature. However, numerical methods based on continuous modeling methods, such as the finite element method and boundary element method, are difficult for studying the dominant mechanisms of rock failure processes related to micro-crack initiation, propagation, and coalescence [44]. The discrete element method can simulate different arrangements of rock grains, the initiation, propagation, and coalescence of micro-cracks, and obtain the evolution of stress and strain distribution during the process, so it provides a better way for understanding the characteristics and mechanism with more detailed information. Nonetheless, this type of modeling is always adopted to study the influence of temperature on the mechanical behaviors of rock [45; 46], while it is still required to develop an effective method to analyze the temperature variation during the deformation and fracturing process based on discrete element modeling. [PERSON] et al. [47] applied the discrete element method to study the thermal effect in the process of rock failure, considering three kinds of heat, i.e., viscous heat, frictional heat, and breaking heat. In fact, it is believed that the thermoelastic effect [48] should not be ignored. In addition, the heat conduction effect between the rock particles should also be considered in the modeling.