Electrically insulating nanofluids were prepared by dispersing modified graphene oxide nanosheets in an insulating medium (paraffin oil) by means of ultrasonication and without using any surfactant. Graphene oxide (GO) nanosheets were synthesized by an improved Hummers method. To improve the compatibility of the GO nanosheets with the oil, they were functionalized by treating with an alkylamine. After preparing the nanofluids, their properties such as thermal conductivity, viscosity and insulating properties were investigated experimentally at different concentrations. The results demonstrated that the thermal conductivity of the oil is enhanced with the addition of the nanosheets and increases with the increasing concentration. Comparison with other similar studies showed that at very low concentrations, the enhancement of thermal conductivity of nanofluids containing modified GO nanosheets is higher. Furthermore, rheological tests demonstrated that the viscosity of the nanofluids is lower in comparison with base oil, which can be considered as an advantage in terms of their thermal performance. Based on the experiments, it is found that the addition of the nanosheets leads to deterioration of the insulating properties of the oil, but available standards show that the prepared nanofluids are still suitable for use in industrial applications. The experimental results were also compared with the theoretical models. The results show that the Nan's model gives better predictions of the thermal conductivity of these nanofluids in comparison with the classic model of Maxwell.