This research focuses on the study of the thermal properties, microstructure, and rheology of biodegradable poly(3-hydroxybutyrate) (PHB) and copolymers containing 5% and 12% of 3-hydroxyvalerate. The attractiveness of the study of these materials is based primarily on the characteristics of biocompatibility and biodegradability of the materials, for their use as substitutes for conventional polymers and in biomedical applications, for which one needs to understand the relationship between their structure and properties. The materials were studied by infrared spectroscopy, thermogravimetric and differential scanning calorimeter analysis, hot-stage polarized optical microscopy, and rheology. The results showed that PHB is not stable in the molten state thus making melt processing difficult. However, 3-hydroxyvalerate reduced the melting transition but increased the thermal stability, opening up the possibility of melt processing. Rheological studies showed that the copolymers display a linear viscoelastic regime, molten 5% 3-hydroxyvalerate exhibited a predominantly elastic behavior, whereas 12% 3-hydroxyvalerate induced a predominantly viscous behavior.