In multiferroic BiFeO3 thin films grown on highly mismatched LaAlO3 substrates, we reveal the coexistence of two differently distorted polymorphs that leads to striking features in the temperature dependence of the structural and multiferroic properties. Notably, the highly distorted phase quasi-concomitantly presents an abrupt structural change, transforms from a hard to a soft ferroelectric and transitions from antiferromagnetic to paramagnetic at 360+/-20 K. These coupled ferroic transitions just above room temperature hold promises of giant piezoelectric, magnetoelectric and piezomagnetic responses, with potential in many applications fields.