A partially oriented melt-extruded PLA multifilament was false-twist textured to stabilize its structure. Conventional DSC analysis showed a relaxation peak at the end of glass transition. Simultaneous consideration of the TMA curve enabled us to evaluate both the relaxation and the cold crystallisation produced during the DSC scan. The periodic load applied during TMA experiments also enabled us to examine the evolution of Young’s modulus along the glass transition, relaxation and cold crystallisation phenomena. Increases in Young’s modulus and in enthalpy are related because of crystallisation. Texturing increased crystallinity and decreased cold crystallisation of PLA during the DSC scan.