Midgap state-based YBa2Cu3O7−x π-junctions have been fabricated by a focused ion-beam system using 45° symmetric [001] tilt SrTiO3 bicrystal substrates. Measurements, performed by inserting the junctions in a superconducting loop (as a double-phase sensitive test), show both an unconventional nonmonotonic temperature dependence of the Josephson current, with a local minimum at a crossover temperature T* and, around T*, a half flux quantum shift in the critical current versus magnetic field modulations, clear signs of a 0–π crossover with temperature. Such results demonstrate that conventional 45° symmetric grain boundary junctions may have potential for applications, from digital circuits to quantum computing.