## 1 Introduction  
Power transformers, as the key component in transmission and distribution systems, play a significant role in power systems. The average winding temperature (AWTT) and the winding hot-spot temperature (WHSTT) serve as critical parameters for assessing the transformer's state [1; 2; 3; 4]. Elevated AWTT can accelerate the degradation of insulation materials, escalate transformer losses, and compromise insulation strength, increasing the risk of equipment malfunctions and accidents. Therefore, the accurate prediction of AWTT is essential for enabling operation and maintenance personnel to promptly identify potential issues and implement protective measures to ensure safe operation of the transformer [5; 6; 7; 8]. Currently, the methods for predicting the AWTT and WHSTT are mainly following: empirical thermal model method, thermal circuit model method, numerical simulation method, and artificial intelligence method. The most used method for calculating AWTT is the empirical thermal model, as in [9; 10]. This method utilizes one or two differential equations to describe the increase in the AWTT in relation to the top oil temperature. Another method is the thermal circuit equivalent model method. In [11], nonlinear thermal resistance is introduced into the thermal path model to solve the problem of uneven heat transfer inside the transformer, and the temperature rise of the transformer winding is predicted by using this model, and a good calculation result is obtained, providing a new example for studying the hot-spot temperature rise of winding by using the thermal path model. In [12], by discussing the influence of oil viscosity and resistance on thermal resistance, the thermal resistance is redefined, which makes the calculation of thermal resistance more practical and improves the lumped thermal path model. However, both the empirical thermal model and the thermal circuit equivalent model bring challenges because parameters such as winding index, oil index, and thermal constant are typically approximated based on the transformer capacity and cooling methods. Therefore, the accuracy of these models in calculating the AWTT is limited in practical applications. Considering the winding structure and loss distribution comprehensively, numerical simulation analysis enables precise calculation of the AWTT. In [13], the finite element method analyzed the magnetic field and transformer loss, and the finite volume method calculated the temperature distribution, considering material property changes. In [14; 15], scholars studied the influence of parameters such as oil passage size and baffle structure on winding temperature to provide guidance for transformer heat dissipation design. Artificial intelligence algorithms can predict the AWTT accurately by analyzing the operational data, environmental factors, and winding characteristics of the transformers. In [16], a model using the kernel extreme learning machine was created to predict the top layer oil temperature of transformers, accounting for uncertainty and matching measured values. In [17], particle swarm optimization improved this model by considering environmental factors, enhancing prediction accuracy. However, due to the complex and variable operating conditions of the transformers, the current methods for predicting AWTT have some problems. Table 1 shows the inadequacies of existing research methods. The mutual influence of factors such as heat conduction, cooling, and losses within the windings makes it difficult for traditional models to provide accurate simulations. Generally, these models rely on oversimplified assumptions and empirical equations, which do not simulate the complex heat conduction process within transformers effectively. Consequently, the accuracy and reliability of current prediction methods for AWTT are limited. Therefore, it is necessary for further research to address these challenges. The thermal properties and operational mechanisms of oil-immersed transformers are analyzed to address the issues in this paper.