Optical vortex beam has wide applications in areas of optical communication, lidar detection and optical trapping. To increase the operating distance, a high-power vortex laser source is necessary in these applications. However, the purity of the output vortex beam decreases with the pump power increasing due to the thermal effect of the laser medium. Therefore, modal field degeneration induced by thermal effect of laser medium has become a key problem in high-power vortex solid-state laser. To investigate this modal field degeneration, the heat transfer and thermal deformation model of an annular beam end pumped thin-disk vortex laser (Fig. (a)) is established. The phase difference of the thermal effect is calculated based on this model. Then, the quadratic term is separated from the phase difference. The non-quadratic term, as a small perturbation, is substituted into the diffraction integral equation of the laser cavity. The modal field structure is obtained by using the perturbation method. The variations of the modal structure with pump power, absorption coefficient and crystal thickness are investigated for three kinds of laser crystals, i.e. Nd:YAG, Nd:YLF and Nd:YVO ₄. The results show that the modal field under thermal effect presents obvious deviation from the ideal mode at high power, and the modal structure shows that it contains many higher-order radial modes, with the angular mode order unchanged. Hence, the radial modal spectrum is broadened by the thermal effect. For an ideal vortex laser without thermal effect operating on the radial mode order 0 and angular mode order 1, Fig. (b) shows the modal structures with thermal effect under different pump power values with a laser crystal thickness of 1 mm. The ratio of the higher-order modes increases and the modal structure becomes more and more complex with the pump power increasing. The ratios of the ideal mode are 0.99, 0.97, 0.90, 0.79 and 0.61, under the pump power of 10 W, 20 W, 40 W, 60 W and 100 W, respectively. Moreover, the Nd:YVO ₄laser has the largest and the Nd:YAG laser has the smallest modal spectrum broadening under the same pump power. Figure (c) shows the variation of the modal purity with the pump power. The modal purity of the Nd:YVO ₄and the Nd:YLF laser decrease to 0.35 and 0.44 at the pump power of 100 W, respectively. We also investigate the modal structures under different absorption coefficients and crystal thickness values. A larger absorption coefficient or a smaller crystal thickness leads to a larger radial modal spectrum broadening and a smaller modal purity. These results indicate that in the design of high-power thin-disk vortex laser, it is necessary to comprehensively optimize the disk thickness and the absorption coefficient, and consider modal spectrum broadening as well.