In the last years new composite materials made of a metallic glass matrix with embedded nanocrystals have arisen as a promising alternative to the metallic glasses, due to their higher hardness. Although the effects of a partial nano-crystallization onto mechanical and magnetic properties have been widely investigated, nothing is known about thermal transport properties, interesting for recently proposed novel applications. Here we investigate how thermal transport is modified in presence of nanocrystalline inclusions in a Zr-based bulk metallic glass. By means of electric measurements and inelastic x ray scattering we are able to disentangle the effects of a partial nanocrystallization onto the two different contributions to heat transport, the electronic and the vibrational one. We show that no enhanced electrons or phonons scattering from the interfaces is observed, while the presence of crystalline nanoinclusions leads to an increase of both contributions, via an increased electric conductivity and transverse acoustic speed of sound. Surprisingly, while a gradual modification of the electric conductivity with the crystalline fraction is observed, even a low crystalline fraction is sufficient to modify elastic and vibrational properties. Our results indicate that low crystallinity composites are indeed promising alternative to both amorphous and crystalline alloys, thanks to their unique combination of high ductility, polycrystal-like vibrational properties and amorphous-like electric transport.