A nanofluid (NF) is composed of a base liquid and suspended nanoparticles (NPs). High-performance NFs exhibit significantly better heat conductivities, as compared to their base liquids. In the present work, we applied all-atom molecular dynamics (MD) simulations to characterize diffusive and ballistic energy transfer mechanisms within nanodiamonds (NDs), carbon nanotubes (CNTs), and N-butylpyridinium tetrafluoroborate ionic liquid (IL). We showed that heat transfer within both NDs and CNTs is orders of magnitude faster than that in the surrounding IL, whereas diffusion of all particles in the considered NF is similar. Intramolecular heat transfer in NPs is a key factor determining the difference of NFs from base liquids. Solvation free energy of NDs and CNTs in ILs was estimated from MD simulations. The geometric dimensions of NPs were shown to be a major source of entropic penalty. Temperature adjusts the entropic factor substantially by modifying a genuine local structure of the bulk base liquid. Our work contributes to engineering more stable and productive suspensions of NPs in ILs, which are necessary for essential progress in the field of NFs.