In this paper, the thermal conductivity behavior of synthetic and natural esters reinforced with 2D nanostructures—single hexagonal boron nitride (h-BN), single molybdenum disulfide (MoS2), and hybrid h-BN/MOS2—were studied and compared to each other. As a basis for the synthesis of nanofluids, three biodegradable insulating lubricants were used: FR3TM and VG-100 were used as natural esters and MIDEL 7131 as a synthetic ester. Two-dimensional nanosheets of h-BN, MoS2, and their hybrid nanofillers (50/50 ratio percent) were incorporated into matrix lubricants without surfactants or additives. Nanofluids were prepared at 0.01, 0.05, 0.10, 0.15, and 0.25 weight percent of filler fraction. The experimental results revealed improvements in thermal conductivity in the range of 20–32% at 323 K with the addition of 2D nanostructures, and a synergistic behavior was observed for the hybrid h-BN/MoS2 nanostructures.