Visual simultaneous localization and mapping (SLAM) systems perform poorly or even fail to work under extreme conditions such as insufficient light, smoke, and fog, and the infrared camera has stronger anti-interference ability in these challenging scenes. However, the high noise and poor imaging quality of infrared camera severely affect the performance of infrared SLAM. Considering the imaging characteristics of the infrared camera and the weak-texture features of subterranean structured scenes, a point-line combined thermal-inertial SLAM system (TPL-SLAM) is proposed. To improve the computational efficiency of point-line combined SLAM, a superior ELSED algorithm is employed to extract line features. Meanwhile, a 3 degrees-of-freedom (DOF) line feature optical flow tracking algorithm is proposed to track line features between continuous frames. Then, the back-end module optimizes inertial measurement unit (IMU), point, and line feature factors in real-time based on a sliding window and jointly performs loop detection with the point and line features on keyframes. Extensive experiments were conducted on real-world datasets to validate the effectiveness of TPL-SLAM. The results showed that TPL-SLAM outperformed the current advanced monocular visual-inertial system (VINS). Besides, parallel loop detection with point-line features can effectively reduce the risk of false loops. The computational efficiency of the proposed line feature extraction and tracking module is superior to those of PL-VINS and EPLF-VINS and can meet the requirements of real-time operation. The data and code for line feature processing are accessible at https://github.com/Fireflyatcode/TPL_SLAM.