Based on the non-equilibrium molecular dynamics simulations, we have studied the thermal conductivities of a novel ultra-thin one-dimensional carbon nanomaterial – diamond nanothread (DNT). Unlike single-wall carbon nanotube (CNT), the existence of the Stone-Wales (SW) transformations in DNT endows it with richer thermal transport characteristics. There is a transition from wave-dominated to particle-dominated transport region, which depends on the length of poly-benzene rings. However, independent of the transport region, strong length dependence in thermal conductivity is observed in DNTs with different lengths of poly-benzene ring. The distinctive SW characteristic in DNT provides more to tune the thermal conductivity not found in the homogeneous structure of CNT. Therefore, DNT is an ideal platform to investigate various thermal transport mechanisms at the nanoscale. Its high tunability raises the potential to design DNTs for different applications, such as thermal connection and temperature management.