  The effects of thermal diffuse scattering on the transmission and eventual
diffraction of highly accelerated electrons are investigated with a method that
incorporates the frozen phonon approximation to the exact numerical solution of
the time-dependent Schr\"odinger equation. Unlike other methods in the related
literature, in this approach the attenuation of diffraction features arises in
a natural way by averaging over a number of wave-packet realizations, thus
avoiding any additional experimentally obtained Debye-Waller factors or
artificial modulations. Without loss of generality, the method has been applied
to analyze the transmission of an electron beam through a thin Al film in two
dimensions, making use of Einstein's model to determine the phonon
configuration for each realization at a given temperature. It is shown that, as
temperature and hence atomic vibration amplitudes increase, incoherence among
different electron wave-function realizations gradually increases, blurring the
well-defined diffraction features characterizing the zero-temperature
intensity.
