We report on the use of femtosecond electron diffraction to resolve the dynamics of electron-phonon relaxation in silicon. Nanofabricated free-standing membranes of polycrystalline silicon were excited below the damage threshold with 387 nm light at a fluence of 5.6 mJ/cm(2) absorbed (corresponding to a carrier density of 2.2 x 10(21) cm(-3)). The diffraction pattern was captured over a range of delay times with a time resolution of 350 fs. All of the detected Bragg peaks exhibited intensity loss with a time constant of less than 2 ps. Beyond the initial decay, there was no further change in the diffracted intensity up to 700 ps. We find that the loss of intensity in the diffracted orders is accounted for by the Debye-Waller effect on a time scale indicative of a thermally driven process as opposed to an electronically driven one. Furthermore, the relaxation time constant is consistent with the excitation regime where the phonon emission rate is reduced due to carrier screening.