  A detailed discussion of the coherent and incoherent dynamic structure
function of the free Fermi gas at finite temperature is presented. Their
behavior and evolution with the momentum transfer and the temperature is
analyzed, while particular attention is paid to the way in which their relative
contribution changes with respect to the $\tilde{T}=0$ case. The influence of
thermal effects on the lowest order sum rules of the coherent and incoherent
responses is also discussed. Finally, the scaling properties of the responses
at high momentum transfer as a function of the temperature are also analyzed.

Soft Condensed Matter;Statistical Mechanics