Abstract: The use of boron nitride nanotubes (BNNTs) for fabrication of thermally conductive composites has been explored in the last years. Their elevated thermal conductivity and high mechanical properties make them ideal candidates for reinforcement in polymeric matrices. However, due to their high tendency to agglomerate, a physical or chemical treatment is typically required for their successful incorporation into polymer matrices. Our previous study about the dispersibility of BNNTs allowed determination of good solvents for dispersion. Here, we performed a similar characterization on styrene-butadiene rubber (SBR) to determine its solubility parameters. Although these two materials possess different solubility parameters, it was possible to bridge this gap by employing a binary mixture. The solvent casting approach followed by hot pressing was chosen as a suitable method to obtain thermally conductive SBR/BNNT composites. The resulting nanocomposites showed up to 35% of improvement in thermal conductivity and a 235% increase in storage modulus in the frequency sweep, when a BNNT loading of 10 wt% was used. However, the viscoelastic properties in the amplitude sweep showed a negative effect with the increase in BNNT loading. A good balance in thermal conductivity and viscoelastic properties was obtained for the composite at a BNNT loading of 5 wt%.