A series of segmented multiblock copolymers containing aramid hard segments and extended polycaprolactone soft segments (with an Mn of 4,200 or 8,200 g mol–1) was prepared and tested for their shape-memory properties. Chain extenders were essential to raise the hard segment concentration so that an extended rubbery plateau could be observed. Dynamic mechanical thermal analysis provided a useful guide in identifying (i) the presence of a rubbery plateau, (ii) the flow temperature, and (iii) the temperature when samples started to deform irreversibly.