  Thermal excitations typically reduce the electric polarization in
ferroelectric materials. Here, we show by means of first-principles
calculations that multiferroic BiFe$_{1-x}$Co$_{x}$O$_{3}$ solid solutions with
$0.25 \le x \le 0.50$ (BFCO) represent a noteworthy exception to this
behaviour. In particular, we find that at room temperature and for moderate
pressures of $0.1$-$1.0$ GPa, depending on the composition, the electric
polarization of bulk BFCO increases by $\sim 200$%. The origin of such an
exceptional behavior is a phase transformation involving a low-$T$ rhombohedral
(${\cal R}$) phase and a high-$T$ super-tetragonal (${\cal T}$) phase. Both
${\cal R}$ and ${\cal T}$ phases are ferrimagnetic near room temperature with
an approximate net magnetization of $0.13$$\mu_{B}$ per formula unit.
Contrarily to what occurs in either bulk BiFeO$_{3}$ or BiCoO$_{3}$, the ${\cal
T}$ phase is stabilized over the ${\cal R}$ by increasing temperature due to
its higher vibrational entropy. This extraordinary $T$-induced ${\cal R} \to
{\cal T}$ phase transition is originated by polar phonon modes involving
concerted displacements of transition-metal and oxygen ions.
