Strong spin-lattice coupling in condensed matter gives rise to intriguing physical phenomena such as colossal magnetoresistance and giant magnetoelectric effects. The phenomenological hallmark of such a strong spin-lattice coupling is the manifestation of a large anomaly in the crystal structure at the magnetic transition temperature. Here we report that the magnetic Néel temperature of the multiferroic compound BiFeO(3) is suppressed to around room temperature by heteroepitaxial misfit strain. Remarkably, the ferroelectric state undergoes a first-order transition to another ferroelectric state simultaneously with the magnetic transition temperature. Our findings provide a unique example of a concurrent magnetic and ferroelectric transition at the same temperature among proper ferroelectrics, taking a step toward room temperature magnetoelectric applications.