In this study, thermal conducting characteristics of a novel hybrid nanostructure consisting of covalently bonded graphene nanoribbon units with/without fullerenes are investigated by performing reverse non-equilibrium molecular dynamics simulations. Simulation results imply that the proposed nanostructure presents significant thermal conducting performance with an isotropic thermal behavior despite the anisotropic thermal characteristics of graphene nanoribbons. Furthermore, thermal conductivity (TC) of the network specimens are shown to be considerably influenced by the ambient temperature and the strain state of the specimen. As an important finding, a significant relationship between the tensile strengths of the structures and their TC values is presented. Furthermore, it is also demonstrated that the deteriorating effect of the fullerenes on thermal conducting performance depends on the size of the welded GNRs as well as the number of the fullerenes within the network. Based on the comparisons with the other carbon based nanostructured network materials, the proposed carbon based hybrid foam-like structure is nominated as a favorable material for thermal applications owing to its remarkable thermal conducting performance accompanied with its ultra-lightweight and high toughness.