The numerical analysis for the controllability assessment of a new design nuclear reactor is typically carried out by means of complex multiphysics codes, solving high fidelity partial differential equations governing the system neutronics as well as the fluid dynamics. Multiphysics codes deliver very accurate solutions at the expense of high computational times, which could be of several hours depending on the specific case study. In this work, to efficiently reduce runtimes, a sensitivity analysis (SA) is carried out to identify the most important input parameters affecting the solution of a multiphysics model developed for the controllability assessment of molten salt reactors (MSRs). The numerical modeling of these innovative systems is fundamental to allow for a safer and more sustainable power production (e.g., due to the lower radiotoxicity of the actinide inventory in MSRs and to the possibility of operation at atmospheric pressure). In this paper, four global sensitivity measures are calculated first, including the Pearson correlation coefficient, δ, Kolmogorov–Smirnov and Kuiper indices, whose results are aggregated by an ensemble strategy and confirmed by the CUmulative SUm of NOrmalized Reordered Output (CUSUNORO) plot. The results of the SA point out that the fuel density is the most important parameter yielding the largest variations in the system reactivity, fundamental for guaranteeing the MSR controllability. In light of this result, a simplified, surrogate model is then developed, which uses density as the only input parameter to determine reactivity, guaranteeing runtime reductions from several hours to a few seconds and, at the same time, a comparable level of accuracy of the multiphysics model. This result demonstrates the capability of global sensitivity analysis approaches to effectively identify the most relevant parameters in MSR systems, supporting the development of simplified, control-oriented models for these innovative reactors.