The present study aimed at developing new thermally responsive shape-memory composites, that were fabricated by Compacting mats of electrospun poly(vinyl alcohol) (PVA) fibers and sheets of a thermoplastic polyether block amide elastomer (PEBA). This design was based on the expectation that the combination of the rubber elasticity of the PEBA matrix and the mechanical switching exploitable through the reversible glass transition temperature (T-g) of the PVA filler could be combined to create material's that display shape memory characteristics as an emergent effect. Dynamic mechanical analyses (DMA) show that, upon introduction of 10-20% w/w PVA fibers, the room-temperature storage modulus (E') increased by a factor of 4-5 in comparison to the neat PEBA, and they reveal a stepwise reduction of E' around the T-g of PVA (85 degrees C). This transition could indeed be utilized to fix a temporaiy shape and recover the permanent shape. At:low strain, the fixity was 66 +/- 14% and the recovery was 98 +/- 2%. Overall, the data validate a simple and practical strategy for the fabrication of shape memory composites that involves a melt compaction process and employs two commercially available polymers.