Recent publication shows that Cu2Se have a peak zT value above 2.0 at 400 K during the second-order phase transitions. One of the reason for such high zT is the great reduction in lattice thermal conductivity, which is strongly supported by the giant reduction in the measured thermal diffusivity. In order to understand the mechanism of such thermal diffusivity reductions, we built a model for the heat transport during phase transitions. The result shows that the reduction in thermal diffusivity is mainly attributed to the coupling between phonons and phase transition. Such large reduction is only occurred when the phase transition is fast. In experiment, the thermal diffusivities and phase transitions of Ag2Se, Cu2Se, and Cu2S were measured. The dramatic thermal diffusivity reductions were only observed in Cu2Se, and Cu2S because they have fast phase transitions, which is consistent with our model.