Composites with carbon nanotubes are becoming increasingly used in energy storage and electronic devices, due to incorporated excellent properties from carbon nanotubes and polymers. Although their properties make them more attractive than conventional smart materials, their electrical properties have been found to be temperature-dependent which is important to consider for the design of devices. To study the effects of temperature in electrically conductive multi-wall carbon nanotube/epoxy composites, thin films were prepared and the effect of temperature on the resistivity, thermal properties and Raman spectral characteristics of the composite films was evaluated. Resistivity-temperature profiles showed three distinct regions in as-cured samples and only two regions in samples whose thermal histories had been erased. In the vicinity of the glass transition temperature, the as-cured composites exhibited pronounced resistivity and enthalpic relaxation peaks, which both disappeared after erasing the composites' thermal histories by temperature cycling. Combined DSC, Raman spectroscopy, and resistivity-temperature analyses indicated that this phenomenon can be attributed to the physical aging of the epoxy matrix and that, in the region of the observed thermal history-dependent resistivity peaks, structural rearrangement of the conductive carbon nanotube network occurs through a volume expansion/relaxation process. These results have led to an overall greater understanding of the temperature-dependent behaviour of conductive carbon nanotube/epoxy composites, including the positive temperature coefficient effect.