The use of lead-free ceramic film materials with positive temperature coefficient of resistivity (PTCR) is widespread in temperature heaters and sensors in micro-electromechanical systems. In this research, the out of plane transport properties of the BiFeO3 (BFO) films have been studied. Surprisingly, PTCR was found in the BFO ceramic films due to the strongly correlated interaction between the multiferroic material BFO and the superconductor YBCO perovskite oxides. To our knowledge, this is the first report on the PTCR effect of BFO films. The BFO/YBCO interface and the bulk conductivity of BFO are important for the PTCR effect, as they make it possible to compare the transport properties of Au/BFO/YBCO- and YBCO/BFO/YBCO-type structures. PTCR was observed in Au/BFO/YBCO at a bias voltage of more than 2 V, but not in the YBCO/BFO/YBCO, even with a 40 V bias voltage. PTCR was found after BFO breakdown of a YBCO/BFO/YBCO capacitor. This indicated that the conductivity of BFO is critical for PTCR. The dependence of PTCR on the superconducting transition temperature illustrates that a cooper-pair can be injected into BFO. Our work presents a method by which to produce a lead-free ceramic film material with PTCR.