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International audience; This paper presents experimental and theoretical results on the temperature-dependent optical response of a single crystal of bismuth to excitation by femtosecond laser pulses. We demonstrate that the measured damping rate of the transient reflectivity oscillations relates to the lifetime of optical phonons. The lifetime is the inverse rate of the decay of optical phonons into two acoustic phonons. This lifetime also indicates the approach to the vibration instability (catastrophe) threshold that manifests the beginning of the disordering of a solid crystal and transition to a liquid state. We observe the red shift of phonon frequency, which increases with the rise of the initial lattice temperature. The red shift is different from the previously observed red shift proportional to the electron temperature, and thus to the excitation laser fluence. The coherent phonon excitation process imprinted into the initial change in the reflectivity and the following reflectivity oscillations allowed us to uncover the temporal phonon history preceding the structural transformation of solid Bi.