  By means of first principles calculations, we computed the effective
electron-phonon coupling constant $G_0$ governing the electron cooling in
photoexcited bismuth. $G_0$ strongly increases as a function of electron
temperature, which can be traced back to the semi-metallic nature of bismuth.
We also used a thermodynamical model to compute the time evolution of both
electron and lattice temperatures following laser excitation. Thereby, we
simulated the time evolution of (1 -1 0), (-2 1 1) and (2 -2 0) Bragg peak
intensities measured by Sciaini et al [Nature 458, 56 (2009)] in femtosecond
electron diffraction experiments. The effect of the electron temperature on the
Debye-Waller factors through the softening of all optical modes across the
whole Brillouin zone turns out to be crucial to reproduce the time evolution of
these Bragg peak intensities.
