Molten salts act as fuel carriers and coolants in liquid-fueled molten salt reactors (MSRs), characterized by strong coupling between neutronics and thermal hydraulics (N-TH) in practical MSR operations. In this study, an in-house light water reactor static and transient analysis code, RESTA-3D, has been extended and applied to MSR transient safety analysis. A parallel multi-channel TH model and a neutron kinetics model incorporating the transport of delayed neutron precursors were implemented into RESTA-3D to account for the MSR-specific N-TH coupling characteristics. Few-group cross-section parameters were generated by the TMSR-LINK code and tabulated for use in RESTA-3D to support MSR transient analysis. The code system was verified against simulation results from well-established MSR dynamics codes and validated against experimental data from the MSRE (Molten Salt Reactor Experiment), covering steady-state temperature distributions, fuel pump-driven transients, and the MSRE natural convection test. Good agreement of the improved RESTA-3D results with the experiment data of MSRE was confirmed, with key parameters such as temperature within a 1% deviation margin, thereby confirming that RESTA-3D is suitable for MSR dynamics analysis. Furthermore, this code was applied to assess the transient characteristics of a 2 MWth thorium-based molten salt reactor (TMSR). The core characteristics, including the inlet fuel overcooling and overheating, unprotected fuel pump start-up and coast-down, were simulated and discussed, indicating that the 2 MWth TMSR design possesses high inherent safety.