  We investigate temperature smearing effects on the electron-boson spectral
density function ($I^2\chi(\omega)$) obtained from optical data using a maximum
entropy inversion method. We start with two simple model input
$I^2\chi(\omega)$, calculate the optical scattering rates at selected
temperatures using the model input spectral density functions and a generalized
Allen's formula, then extract back $I^2\chi(\omega)$ at each temperature from
the calculated optical scattering rate using the maximum entropy method (MEM)
which has been used for analysis of optical data of high-temperature
superconductors including cuprates, and finally compare the resulting
$I^2\chi(\omega)$ with the input ones. From this approach we find that the
inversion process can recover the input $I^2\chi(\omega)$ almost perfectly when
the quality of fits is good enough and also temperature smearing (or thermal
broadening) effects appear in the $I^2\chi(\omega)$ when the quality of fits is
not good enough. We found that the coupling constant and the logarithmically
averaged frequency are robust to the temperature smearing effects and/or the
quality of fits. We use these robust properties of the two quantities as
criterions to check whether experimental data have intrinsic
temperature-dependent evolutions or not. We carefully apply the MEM to two
material systems (one optimally doped and the other underdoped cuprates) and
conclude that the $I^2\chi(\omega)$ extracted from the optical data contain
intrinsic temperature-dependent evolutions.
