Different nanoscale fillers have been used to create composite fluids for applications such as thermal management. The ever increasing thermal loads in applications now require advanced operational fluids, for example, high thermal conductivity dielectric oils in transformers. These oils require excellent filler dispersion, high thermal conduction, but also electrical insulation. Such thermal oils that conform to this thermal/electrical requirement, and yet remain in highly suspended stable state, have not yet been synthesized. We report here the synthesis and characterization of stable high thermal conductivity Newtonian nanofluids using exfoliated layers of hexagonal boron nitride in oil without compromising its electrically insulating property. Two-dimensional nanosheets of hexagonal boron nitride are liquid exfoliated in isopropyl alcohol and redispersed in mineral oil, used as standard transformer oil, forming stable nanosuspensions with high shelf life. A high electrical resistivity, even higher than that of the base oil, is maintained for the nano-oil containing small weight fraction of the filler (0.01 wt %), whereas the thermal conductivity was enhanced. The low dissipation factor and high pour point for this nano-oil suggests several applications in thermal management.