In this talk, we reveal quantitatively the hybrid heat-wave nature of the flow generated by the heat equation with memory. This nature shows in more detail: First, the flow exhibits the propagation of singularities along the time-direction; Second, the flow exhibits a finite order smoothing effect; third, when t > 0, the flow is dominated by the wave-like nature, while when t → 0, the heat-like nature plays an increasingly important role in the flow. The above-mentioned nature is given by an explicit decomposition of the flow.