This work presents a time dependent version of the fission matrix method named Transient Fission Matrix (TFM) developed to perform kinetics calculations. Coupled neutronics and thermal-hydraulics transient calculations are studied using the TFM approach and a Computational Fluid Dynamics (CFD) code. The generation of the matrices is performed using the Monte Carlo neutronic code SERPENT beforehand the transient calculation. The neutronic module and the coupling are directly implemented in the CFD opensource code OpenFOAM. An application case is presented on the Molten Salt Fast Reactor (MSFR). This system is a circulating liquid fuel reactor characterized by a two meter core cavity and a fast spectrum. Thus the present approach is well suited since an accurate distribution of the velocity of the liquid fuel circulating in the cavity and of the delayed neutron precursor transport is required. A reactivity insertion incident of around 2.5$ is presented, showing the good behavior of the MSFR in such a case. A load-following from 50% to the nominal power generation is also discussed