We report on the synthesis and characterization of BiFe${}_{0.5}$Mn${}_{0.5}$O${}_{3}$, a potential type-I multiferroic compound displaying temperature-induced magnetization reversal. Bulk samples were obtained by means of solid-state reaction carried out under the application of hydrostatic pressure of 6 GPa at 1100 \ifmmode^\circ\else\textdegree\fi{}C. The crystal structure is a highly distorted perovskite with no cation order on the $B$ site, where, besides a complex scheme of tilt and rotations of the TM-O${}_{6}$ octahedra, large off-centering of the bismuth ions is detected. Below ${T}_{1}$ $=$ 420 K the compound undergoes a first weak ferromagnetic transition related to the ordering of iron-rich clusters. At lower temperatures (just below RT) a complex thermally activated mechanism induces at first an enhancement of the magnetization at ${T}_{2}$ $=$ 288 K, then a spontaneous reversal giving rise to a negative response. The complementary use of powder neutron diffraction, superconducting quantum interference device magnetometry, and M\"ossbauer spectroscopy allowed us to propose as a possible interpretation of the overall magnetic behavior the presence of an uncompensated competitive coupling between nonequivalent clusters of weakly ferromagnetic interactions characterized by different critical temperatures and resultant magnetizations.