We have investigated the structural response of melt-spun poly-3-hydroxybutyrate (P3HB) fibers to stress and temperature and its impact on the mechanical properties. Low-stress (<= 1.6 MPa, 100-130 degrees C) annealed P3HB fibers showed a considerable viscoelastic behavior and remained ductile up to at least two months. Stress annealing with high weights (>= 32 MPa), however, lead to fibers with a higher tensile strength (182 MPa) and with a lower elongation at break (22%). These significant differences in the tensile properties are closely related to structural changes, which we have studied with in-situ wide-angle x-ray diffraction (WAXD) and small-angle x-ray scattering (SAXS) experiments. A highly oriented non-crystalline mesophase (P-nc), which is located in-between orthorhombic alpha-crystals is growing during high-stress annealing but disappears during low-stress annealing. However, it is possible to restore the mesophase by post-drawing. The viscoelastic hysteresis behavior of low-stress annealed fibers is explained by a reversible transformation of a-crystals into mesophase and back.