Thin film thermometers made from pencil lead have been used successfully as ballistic phonon sensors on insulating crystals because of their low heat capacity and rapid response time [1]. We have characterized the d.c. conductivity of these devices in the temperature range from 2 mK to 500 mK as a preliminary step in our program to develop a new type of particle detector which senses ballistic phonons created by the collision of an incident particle with an electron or nucleus in a silicon crystal. Strong deviations from ohmic conductivity have been observed in the limit of ultralow temperature and low electric field.The effect is attributed to electric field enhanced hopping of electrons between shallow wells either due to effective reduction of the tunneling barrier or else to thermal activation caused by heating.