Some materials show an abrupt increase in resistivity when the temperature changes only over a few degrees. This phenomenon, known as PTCR effect (positive temperature coefficient of resistivity), has been largely studied in the last few years, due to its potential applications in industry. Particularly, it can be used in auto controlled heaters, temperature sensors, protection circuits and in security systems for power electronic circuits. In this work we present the study of the electrical properties of the percolating system carbon black particles filled with ethylene butylacrylate copolymer composite (EBA), in the temperature range from −100 to 100 °C and in frequencies between 10 Hz and 100 kHz. The PTCR effect was observed at temperatures slightly above the room temperature, for concentrations higher than that of the percolation critical concentration. The mechanism responsible for the change in resistivity, at this stage, is predominantly tunnelling, wherein the conductive filler particles are not in physical contact, and the electrons tunnel through the insulating gap between them. At low temperatures, such as below and close to the glass transition temperature, the DC conductivity obeys the Arrhenius law. The calculated activation energy values are independent of carbon black contents inside the copolymer matrix, suggesting that these particles do not interact significantly with the chain segments of the macromolecules in the EBA copolymer.