Thermal transport in carbon nanofibers (CNFs) was thoroughly investigated. In particular, individual CNFs were suspended on T-type heat nanosensors and their thermal conductivity was measured over a range of temperatures. Unexpectedly, thermal conductivity was found to be dependent on CNF wall thickness and ranging between ca. 28 and 43 W/(m⋅K). Further investigation of the CNF walls with high resolution electron microscopy allowed us to propose a tentative description of how wall structure affects phonon heat transport inside CNFs. The lower thermal conductivities, compared to other CNTs, was attributed to unique CNF wall structure. Additionally, wall thickness is related to the conducting lattice length of each constituent graphene cone and comparable to the Umklapp length. Hence, as the wall thickness and thus lattice length increases there is a higher probability for phonon scattering to the next layer.