  Although high energetic radiation from flares is a potential threat to
exoplanet atmospheres and may lead to surface sterilization, it might also
provide the extra energy for low-mass stars needed to trigger and sustain
prebiotic chemistry. We investigate two flares on TRAPPIST-1, an ultra-cool
dwarf star that hosts seven exoplanets of which three lie within its habitable
zone. The flares are detected in all four passbands of the MuSCAT2 allowing a
determination of their temperatures and bolometric energies. We analyzed the
light curves of the MuSCAT1 and MuSCAT2 instruments obtained between 2016 and
2021 in $g,r,i,z_\mathrm{s}$-filters. We conducted an automated flare search
and visually confirmed possible flare events. We studied the temperature
evolution, the global temperature, and the peak temperature of both flares. For
the first time we infer effective black body temperatures of flares that
occurred on TRAPPIST-1. The black body temperatures for the two TRAPPIST-1
flares derived from the SED are consistent with $T_\mathrm{SED} =
7940_{-390}^{+430}$K and $T_\mathrm{SED} = 6030_{-270}^{+300}$K. The flare
black body temperatures at the peak are also calculated from the peak SED
yielding $T_\mathrm{SEDp} = 13620_{-1220}^{1520}$K and $T_\mathrm{SEDp} =
8290_{-550}^{+660}$K. We show that for the ultra-cool M-dwarf TRAPPIST-1 the
flare black body temperatures associated with the total continuum emission are
lower and not consistent with the usually adopted assumption of 9000-10000 K.
This could imply different and faster cooling mechanisms. Further multi-color
observations are needed to investigate whether or not our observations are a
general characteristic of ultra-cool M-dwarfs. This would have significant
implications for the habitability of exoplanets around these stars because the
UV surface flux is likely to be overestimated by the models with higher flare
temperatures.
