Centaurs are believed to be Kuiper Belt objects in transition between Jupiter and Neptune before possibly becoming Jupiter family comets. Some indirect observational evidence is consistent with the presence of amorphous water ice in Centaurs. Some of them also display a cometary activity, probably triggered by the crystallization of the amorphous water ice, as suggested by Jewitt and this work. Indeed, we investigate the survival of amorphous water ice against crystallization, using a fully three-dimensional thermal evolution model. Simulations are performed for varying heliocentric distances and obliquities. They suggest that crystallization can be triggered as far as 16 AU, though amorphous ice can survive beyond 10 AU. The phase transition is an efficient source of outgassing up to 10-12 AU, which is broadly consistent with the observations of the active Centaurs. The most extreme case is 167P/CINEOS, which barely crystallizes in our simulations. However, amorphous ice can be preserved inside Centaurs in many heliocentric distance-obliquity combinations, below a ∼5-10 m crystallized crust. We also find that outgassing due to crystallization cannot be sustained for a time longer than 10 4 -10 4 years, leading to the hypothesis that active Centaurs might have recently suffered from orbital changes. This could be supported by both observations (although limited) and dynamical studies.