## 1 Introduction  
With the continuous development of modern industry, pipes with anisotropic materials are widely used in the aerospace and transportation fields by virtue of their strong comprehensive performance, which often requires service under high-temperature conditions. For example, in the aerospace industry, these pipes are subjected to extreme temperatures in the engine. The probability of thermal stress, corrosion, and cracking in a high-temperature environment is much higher than that in a normal-temperature environment. These phenomena seriously affect the function and life of the equipment. Ultrasonic guided waves can achieve rapid non-destructive testing of pipeline defects with local removal of insulation and anti-corrosion layers. A previous study has shown that the coupling of the temperature and strain fields have an effect on the wave propagation speed and waveform [1]. It can be seen that in order to realize the online detection of guided waves in high-temperature pipes, accurately obtaining the propagation characteristics of guided waves under the temperature field is an important prerequisite for realizing the characterization of defects in the structures. Currently, there are some methods to calculate the dispersion characteristics of guided waves in hollow cylinders. Among them, the transfer matrix and global matrix methods [2], which are based on the sub-wave expansion method, have been widely used in many materials as well as computational cases. However, the transfer matrix has the problem of numerical instability when solving large frequency-thickness products. Although the global matrix method solves the problem of numerical instability, it may take a long time to compute when the matrix is too large. To overcome the above problems, [PERSON] et al. [3] investigated the propagation characteristics of guided waves in multilayer piezoelectric material plates using [PERSON]'s orthogonal polynomial expansion method, which converts the traditional problem of solving transcendental equations into an eigenvalue problem by expanding the displacements into a polynomial series. After that, [PERSON] et al. [4, 5] solved the propagation characteristics of circumferential guided waves in a multilayer piezoelectric cylindrical plate and longitudinal guided waves in a multilayer hollow cylinder by using improved Legendre polynomials. [PERSON] et al. [6] investigated the axial guided wave characteristics of piezoelectric cylinders using [PERSON]'s series method. [PERSON] et al. [7] obtained complete dispersion curves in complex domains based on [PERSON]'s polynomial method with stress and potential shift expansion. [PERSON] et al. [8, 9] solved longitudinally guided waves in anisotropic hollow cylinders as well as circumferentially guided waves in multilayer composite hollow cylinders based on state vectors and Legendre orthogonal polynomials. Simultaneously, it has been found that changes in the temperature field also have an effect on the propagation characteristics of sound waves. While there is an assumption of infinite velocity in the classical theory of heat conduction in solids, which is contrary to physical phenomena, various generalized thermoelastic theories have been developed. Among them, the LS model, the GL model, and the GN model [10] are the more classical models, and based on these thermoelastic theories, many researchers have investigated the propagation characteristics of thermoelastic waves. [PERSON] et al. [11] investigated the dispersion characteristics of guided waves in isotropic plates based on GL theory and GN generalized thermoelastic theory. [PERSON] et al. [10] investigated the thermoelastic guided waves in transverse isotropic plates based on LS theory by using the semi-analytical finite element method. Based on GN theory, [PERSON] et al. [12] uses the finite element method to improve the formula and numerically analyzes the dispersion characteristics of guided waves in hollow cylinder structures. [PERSON] et al.