Fused deposition modelling (FDM) is a process of additive manufacturing allowing creating of highly precise complex three-dimensional objects for a large range of applications. The principle of FDM is an extrusion of the molten filament and gradual deposition of layers and their solidification. Potential applications in pharmaceutical and medical fields require the development of biodegradable and biocompatible thermoplastics for the processing of filaments. In this work, the potential of production of poly(3-hydroxybutyrate-co-4-hydroxybutyrate) (P(3HB-co-4HB)) filaments for FDM was investigated in respect to its thermal stability. Copolymer P(3HB-co-4HB) was biosynthesised by Cupriavidus malaysiensis. Rheological and mechanical properties of the copolymer were modified by the addition of plasticizers or blending with poly(lactic acid). Thermal stability of mixtures was studied employing thermogravimetric analysis and rheological analyses by monitoring the time-dependent changes in the complex viscosity of melt samples. The plasticization of P(3HB-co-4HB) slightly hindered its thermal degradation but the best stabilization effect was found in case of the copolymer blended with poly(lactic acid). Overall, rheological, thermal and mechanical properties demonstrated that the plasticized P(3HB-co-4HB) is a potential candidate of biodegradable polymer for FDM processes.