Predicting the microstructural evolution of radiation damage in materials requires handling the physics of infrequent-events, in which several time scales are involved. The reactions rates characterizing these events are the main ingredient for simulating the kinetics of materials under irradiation over large time scales and high irradiation doses. We propose here an efficient, finite temperature method to compute reaction rate constants of thermally activated processes. The method consists of two steps. Firstly, rare reactive trajectories in phase-space are sampled using a transition path sampling (TPS) algorithm supplemented with a local Lyapunov bias favoring diverging trajectories. This enables the system to visit transition regions separating stable configurations more often, and thus enhances the probability of observing transitions between stable states during relatively short simulations. Secondly, reaction constants are estimated from the unbiased fraction of reactive trajectories, yielded by an appropriate statistical data analysis tool, the multistate Bennett acceptance ratio (MBAR) package. We apply our method to the calculation of reaction rates for vacancy and di-vacancy migration in α-Iron crystal, using an Embedded Atom Model potential, for temperatures ranging from 300 K to 800 K.