Highly flexible biocompatible materials that are both thermally conductive and electrically insulating are important for implantable and wearable bioelectronics applications. The ability to thermally process these materials into useful structures using additive manufacturing approaches opens up new opportunities for its use in bespoke structures. Here we investigate the three-dimensional (3D) printing of a medical-grade thermoplastic polyurethane (PU) elastomer, which is thermally insulating and enhance its thermal and mechanical properties through the incorporation of boron nitride (BN) as a filler. Via a simple solution compounding approach, a highly flexible and thermally conductive BN nanoparticle/ PU composite has been developed and subsequently processed into simple bio-scaffolds structures via a 3D pneumatic melt extrusion printing process. The addition of up to 20% w/w of BN to the PU significantly enhances the tensile modulus by 659%, from 1.74 to 13.2 MPa, while supporting high mechanical flexibility. The thermal conductivity of 20% w/w BN/PU composite increases by 74% with respect to the unmodified PU. The 3D printed BN/PU composite scaffolds exhibit good biocompatibility and cell attachment enhancement with L929 fibroblast cells.