A multi-scale approach, including large-scale molecular dynamics simulations, finite element simulations and analytical effective media modeling, has been adopted to investigate the effects of covalent functionalization on the thermal transport in carbon nanotube (CNT)/polymer composites. It is shown that the cross-links between the polymer and CNTs can further remarkably suppress thermal conductivities of embedded functionalized CNTs by up to 50%, compared with free-standing functionalized CNTs. The cross-links can enhance the thermal coupling between the polymer and CNTs but they also cause density variation in near-interface polymer layers and induce secondary interfacial resistances in the polymer. The thermal coupling between CNTs and polymers mainly occurs on the sidewall of the CNTs and the functionalization will actually shrink the coupling zones. By considering all these effects, an analytical thermal transport model has been developed for the prediction of the effective thermal conductivity of CNT/polymer composites and it shows that overall the functionalization leads to an adverse effect on the thermal transport in the composites. Compared with single-walled CNTs, multi-walled CNTs are less sensitive to these effects, rendering them more suitable as fillers. This study may shed light on the fundamental understanding of the thermal transport in composites with carbon-based fillers such as graphene or graphene oxide. (C) 2014 Elsevier Ltd. All rights reserved.