This paper evaluates the performance of neutronic and thermal-hydraulic coupling algorithms in transient problems based on the high-temperature gas-cooled reactor simulator TINTE. In particular, the operator splitting semi-implicit (OSSI), Picard iteration, and Jacobian-free Newton-Krylov (JFNK) methods are compared by a practical engineering model. The OSSI method is employed in the original TINTE. The fully implicit algorithms TINTE-Picard and TINTE-JFNK are implemented in this study. Several special numerical technologies are discussed to improve the performance of JFNK. First, a novel JFNK variant is employed to deal with the multiscale coupling between local fuel sphere temperature and global solid porous media temperature. Second, the preconditioning strategy is determined by making a balance between performance and code burden. Finally, the scaling modifications of the Jacobian matrix and perturbation size are investigated to solve the ill-posed problem. What is more, the framework of TINTE-Picard and TINTE-JFNK is presented, and the key points of implementation are discussed. Numerical results indicate that the advanced coupling algorithms Picard and JFNK can achieve higher computational performance than the original semi-implicit coupling algorithm in TINTE due to the accuracy and stability advantage.