A biodegradable and biocompatible electrospun scaffold with shape memory behavior in the physiological temperature range is here presented. It was obtained starting from a specifically designed, biobased PLLA-based triblock copolymer, where the central block is poly(propylene azelateco-propylene sebacate) (P(PAz60PSeb40)) random copolymer. Shape memory properties are determined by the contemporary presence of the low melting crystals of the P(PAz60PSeb40) block, acting as switching segment, and of the high melting crystal phase of PLLA blocks, acting as physical network. It is demonstrated that a straightforward annealing process applied to crystal phase of the switching element gives the possibility to tune the shape recovery temperature from about 25 to 50 degrees C, without the need of varying the copolymer's chemical structure. The thermal annealing approach here presented can be thus considered a powerful strategy for "ad hoc" programming the same material for applications requiring different recovery temperatures. Fibroblast culture experiments demonstrated scaffold biocompatibility.