As indicated by theory and experimental measurements individual carbon nanotubes (CNTs) have very high values of thermal conductivity. One of the challenges is to achieve high thermal conductivity in macroscopic assemblies of CNTs such as fibres, films and composites, paving the way to a wide range of applications. CNT fibres have tremendous potential in succeeding as the future materials for a variety of applications when properties at the nanoscale are translated to their macroscopic assemblies. In this paper we report the measurements of thermal conductivity of continuously spun CNT fibres and its dependence on temperature. Thermal conductivity measurements were performed using in-house built temperature sensing microscope probe. Specific thermal conductivity of CNT fibres showed an order of magnitude advantage over the traditional materials used for heat dissipation.