While the dispersion of nanomaterials is known to be effective in enhancing the thermal conductivity and specific heat capacity of fluids, the mechanisms behind this enhancement remain to be elucidated. Herein, we report on highly stable, surfactant-free graphene nanofluids, based on N,N-dimethylacetamide (DMAc) and N,N-dimethylformamide (DMF), with enhanced thermal properties. An increase of up to 48% in thermal conductivity and 18% in specific heat capacity was measured. The blue shift of several Raman bands with increasing graphene concentration in DMF indicates that there is a modification in the vibrational energy of the bonds associated with these modes, affecting all the molecules in the liquid. This result indicates that graphene has the ability to affect solvent molecules at long-range, in terms of vibrational energy. Density functional theory and molecular dynamics simulations were used to gather data on the interaction between graphene and solvent, and to investigate a possible order induced by graphene on the solvent. The simulations showed a parallel orientation of DMF towards graphene, favoring π-π stacking. Furthermore, a local order of DMF molecules around graphene was observed suggesting that both this special kind of interaction and the induced local order may contribute to the enhancement of the fluid's thermal properties.