## 1 Introduction
### Research Background  
Within the background of evaluating equipment health status and service life through behavioral analysis of mechanical systems, DT technology has emerged as an innovative solution. This advanced methodology employs multisensory data acquisition to capture physical parameters from real-world operations, which are subsequently mapped to virtual mathematical models via data interaction and integration protocols. Such implementations enable the simulation of latent risks undetectable in physical domains and extreme operational scenarios that defy conventional monitoring, achieving cost-effective acquisition of equivalent or superior information compared to physical prototypes [4,5]. Current applications of vibration signal-based DT implementations have been extensively deployed in bearing fault diagnosis [6], online monitoring [7], health management [8], and full lifecycle prognosis [9]. The thermally driven behavioral prediction methodologies derived from DT frameworks have been innovatively extended to diverse domains, including architectural structures [10], thermal power generation [11], power electronics modules [12], lithium-ion batteries [13], and electric vehicles [14]. These approaches demonstrate superior prediction accuracy, enhanced robustness, and low parametric dependency, positioning DT as an interdisciplinary research frontier with significant developmental potential.  
The current literature demonstrates limited exploration in predictive methodologies for bearing thermal behaviors. [PERSON] et al. [15] implemented temperature correction models to recalibrate thermal boundaries, achieving digital twin-enabled real-time monitoring of thermal characteristics and health status in motorized spindle bearings. Present research predominantly focuses on refining pure thermal models (virtual layer) through enhanced analytical/numerical approaches for superior temperature computation, exemplified by lumped parameter thermal network (LPTN) [16], finite element (FE), and computational fluid dynamics (CFD) [17,18]. Notably, CFD implementations employing finite volume methods require extensive preprocessing time for 3D model construction and mesh generation. Furthermore, the dynamic phase variations of multiphase media (such as oil-air mixtures in oil lubrication or grease-oil-air mixtures in grease lubrication) within the bearing chamber cavity necessitate advanced techniques like dynamic meshing and user-defined functions (UDFs) for accurate cooling-state simulation and thermal fluid domain analysis. However, the long convergence time during iterative computations remains a critical bottleneck, hindering real-time thermal monitoring and estimation in bearing systems [19,20]. Consequently, the LPTN model approaches persist as conventional tools for bearing thermal analysis, particularly under transient operational conditions. [PERSON] et al. [21] established mathematical models and numerical solutions for heat generation rates in grease-lubricated spherical roller bearings using local heat source analysis. [PERSON] et al. [22] developed thermal network models for grease-lubricated bearings through analysis of load distribution and kinematic parameters in high-speed railway double-row tapered roller bearings. [PERSON] et al. [23] systematically compared enhanced thermal node configuration schemes under different lubrication states and proposed an optimized hybrid LPTN model integrating seven-node and multi-node configurations to investigate thermal disparities in oil-air lubricated angular contact bearings.  
While these advancements have significantly contributed to virtual modeling frameworks and thermal distribution pattern elucidation, persistent challenges remain in existing thermal models regarding long-term durability analysis.