A detailed investigation of the time evolution for the low-field resistance R-off and the threshold voltage V-th in chalcogenide-based phase-change memory devices is presented. It is observed that both R-off and V-th increase and become stable with time and temperature, thus improving the cell readout window. Relying on a microscopic model, the drift of R-off and V-th is linked to the dynamic of the intrinsic traps typical of amorphous chalcogenides, thus providing for the first time a unified framework for the comprehension of chalcogenide materials transient behavior.