A 20MWth, 540 EFPD once through fuel cycle small modular molten salt reactor with solid fuel is proposed by Massachusetts Institute of Technology for off-grid applications. In this paper, various thermal-hydraulic analysis methods including computational fluid dynamics, Reactor Excursion Leak Analysis Program (RELAP5), and DAKOTA are adopted step-by-step for the reactor design based on the neutronic analysis results. First, 1/12th full core thermal hydraulic analysis is performed by using STAR CCM+ with most conservative considerations. Second, the transient safety behaviors of reactor system with risky assumptions are conducted by using REALP5. Finally, due to the unknown factors affecting reactor thermal-hydraulic characteristics, the uncertainty quantification and sensitivity analysis for the designed reactor is performed with DAKOTA code coupled with RELAP5. Numerical results show that a more uniform temperature distribution with reduced peak temperatures of fuel and coolant across the reactor core has been achieved. Enough safety margin is maintained even under most severe transient accident. The uncertainties in the heat transfer coefficient and helium gap conductivity factor are the most remarkable contributors to the statistical results of peaking fuel temperature. All above results preliminarily indicate the feasibility of the current small modular molten salt reactor design and provide the further optimization direction from reactor thermal-hydraulic prospective.