Aims. Stellar flares emit thermal and nonthermal radiation in the X-ray and ultraviolet (UV) regime. 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. Despite the UV continuum emission being constrained partly by the flare temperature, few efforts have been made to determine the flare temperature for ultra-cool M-dwarfs. 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 instrument allowing a determination of their temperatures and bolometric energies. Methods. We analyzed the light curves of the MuSCATl (multicolor simultaneous camera for studying atmospheres of transiting exoplanets) and MuSCAT2 instruments obtained between 2016 and 2021 in g, r, i, z_s-filters. We conducted an automated flare search and visually confirmed possible flare events. The black body temperatures were inferred directly from the spectral energy distribution (SED) by extrapolating the filter-specific flux. We studied the temperature evolution, the global temperature, and the peak temperature of both flares. Results. White-light M-dwarf flares are frequently described in the literature by a black body with a temperature of 9000–10 000 K. 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_SED = 7940₋₃₉₀⁺⁴³⁰ K and T_SED = 6030₋₂₇₀⁺³⁰⁰ K. The flare black body temperatures at the peak are also calculated from the peak SED yielding T_SEDp = 13 620₋₁₂₂₀⁺¹⁵²⁰ K and T_SEDp = 8290₋₅₅₀⁺⁶⁶⁰ K. We update the flare frequency distribution of TRAPPIST-1 and discuss the impacts of lower black body temperatures on exoplanet habitability. Conclusions. 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 9000–10 000 K in the context of exoplanet research. For the peak emission, both flares seem to be consistent with the typical range from 9000 to 14 000 K, respectively. 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.