The enhancement of the thermal conductivity, keeping the electrical insulation, of epoxy thermosets through the addition of pristine and oxidized carbon nanotubes (CNTs) and microplatelets of boron nitride (BN) was studied. Two different epoxy resins were selected: a cycloaliphatic (ECC) epoxy resin and a glycidylic (DGEBA) epoxy resin. The characteristics of the composites prepared were evaluated and compared in terms of thermal, thermomechanical, rheological and electrical properties. Two different dispersion methods were used in the addition of pristine and oxidized CNTs depending on the type of epoxy resin used. Slight changes in the kinetics of the curing reaction were observed in the presence of the fillers. The addition of pristine CNTs led to a greater enhancement of the mechanical properties of the ECC composite whereas the oxidized CNTs presented a greater effect in the DGEBA matrix. The addition of CNTs alone led to a marked decrease of the electrical resistivity of the composites. Nevertheless, in the presence of BN, which is an electrically insulating material, it was possible to increase the proportion of pristine CNTs to 0.25 wt% in the formulation without deterioration of the electrical resistivity. A small but significant synergic effect was determined when both fillers were added together. Improvements of about 750% and 400% in thermal conductivity were obtained in comparison to the neat epoxy matrix for the ECC and DGEBA composites, respectively. © 2019 Society of Chemical Industry