We report on heat conduction properties of thermal interface materials with self-aligning magnetic grapheme fillers. Graphene enhanced nano-composites were synthesized by an inexpensive and scalable technique based on liquid-phase exfoliation. Functionalization of graphene and few-layer-graphene flakes with Fe3O4 nanoparticles allowed us to align the fillers in an external magnetic field during dispersion of the thermal paste to the connecting surfaces. The filler alignment results in a strong increase of the apparent thermal conductivity and thermal diffusivity through the layer of nano-composite inserted between two metallic surfaces. The self-aligning magnetic grapheme fillers improve heat conduction in composites with both curing and non-curing matrix materials. The thermal conductivity enhancement with the oriented fillers is a factor of two larger than that with the random fillers even at the low ~1 wt. % of graphene loading. The real-life testing with computer chips demonstrated the temperature rise decrease by as much as 10oC with use of the non-curing thermal interface material with ~1 wt. % of the oriented fillers. Our proof-of-concept experiments suggest that the thermal interface materials with functionalized graphene and few-layer-graphene fillers, which can be oriented during the composite application to the surfaces, can lead to a new method of thermal management of advanced electronics.