The kinetic of phase transitions under irradiation of MgAl2O4 has been studied using molecular dynamics (MD) simulation by means of continuous cation Frenkel pair (FP) accumulation. Three different cases have been considered: cation FP accumulation starting (i) from the normal (N) spinel, (ii) from the amorphous (A) spinel and (iii) from the interface between rock-salt (NaCl) spinel and A-spinel. When submitted to FP accumulation, the N-spinel transits directly towards the NaCl-spinel for temperature lower than 600K. For temperatures higher than 600K, the dose needed to obtain the rock-salt structure increases with temperature, and the structure transits to an intermediate disordered (D) structure prior to the NaCl-spinel. No amorphization of the spinel under FP accumulation is obtained for doses up to 68 displacements per cation at 30K. The dose - temperature dependence relies on thermally activated FP recombination processes. The epitaxial and homogeneous irradiation induced re-crystallization of amorphous MgAl2O4 was obtained by continuous FP accumulation. Present results point out that the re-crystallization induced by FP accumulation appears in both cases to be thermally enhanced but non diffusive. It is governed by a local rearrangement of each point defect in the homogeneous case, while spontaneous FP recombination process in the crystalline part or at the interface drives the recrystallization in the epitaxial case. In summary, the thermally enhanced - but non diffusive - Frenkel pair recombination or local relaxation of point defects may play a central role to the radiation resistance of MgAl2O4.