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.