A packing assembly for a valve includes a first segment having at least one first guiding surface, and a second segment having at least one second guiding surface in engagement with at least a portion of the at least one first guiding surface. A shape-memory member couples the first and second segments. The shape-memory member may be formed of a material that is responsive to changes in temperature, so that, in response to a change in temperature, the shape-memory member may cause relative movement of the first and second segments in a first direction. In response to the movement, the first and second guiding surfaces may cause relative displacement of the first and second segments in a second direction.