Measurements of the enhancement of the thermal conductivity of an epoxy resin, when reinforced with plies of plain weave glass fabric and by carbon multiwalled nanotubes (C-MWNT) and with both, are presented. The transient hot-wire technique, as it was recently modified to measure the thermal conductivity of solids, was used with an uncertainty of less than +/- 1 %. The results revealed for the epoxy reinforced with glass fibers, with volume fraction of 28 % (47 % weight fraction), the thermal conductivity increase was 27 % compared to plain epoxy resin. When reinforced with C-MWNT, the maximum enhancement observed was about 20 % at it concentration of 1.2 % by weight of C-MWNT. Similarly, when reinforced with both the C-MWNT and glass fibers, the maximum thermal conductivity enhancement observed was about 60 % at a concentration of 1.2 % by weight of C-MWNT.