The pyroresistive response of conductive polymer composites (CPCs) has attracted much interest because of its potential applications in many electronic devices requiring a significant responsiveness to changes in external physical parameters such as temperature or electric fields. Although extensive research has been conducted to study how the properties of the polymeric matrix and conductive fillers affect the positive temperature coefficient pyroresistive effect, the understanding of the microscopic mechanism governing such a phenomenon is still incomplete. In particular, to date, there is little body of theoretical research devoted to investigating the effect of the polymer thermal expansion on the electrical connectivity of the conductive phase. Here, we present the results of simulations of model CPCs in which rigid conductive fillers are dispersed in an insulating amorphous matrix. By employing a meshless algorithm to analyze the thermoelastic response of the system, we couple the computed strain field to the electrical connectedness of the percolating conductive particles. We show that the electrical conductivity responds to the local strains that are generated by the mismatch between the thermal expansion of the polymeric and conductive phases and that the conductor-insulator transition is caused by a sudden and global disconnection of the electrical contacts forming the percolating network.