  We investigate the scattering of intense short laser pulses off trapped cold
fermionic atoms. We discuss the sensitivity of the scattered light to the
quantum statistics of the atoms. The temperature dependence of the scattered
light spectrum is calculated. Comparisons are made with a system of classical
atoms who obey Maxwell-Boltzmann statistics. We find the total scattering
increases as the fermions become cooler but eventually tails off at very low
temperatures (far below the Fermi temperature). At these low temperatures the
fermionic degeneracy plays an important role in the scattering as it inhibits
spontaneous emission into occupied energy levels below the Fermi surface. We
demonstrate temperature dependent qualitative changes in the differential and
total spectrum can be utilized to probe quantum degeneracy of trapped Fermi gas
when the total number of atoms are sufficiently large $(\geq 10^6)$. At smaller
number of atoms, incoherent scattering dominates and it displays weak
temperature dependence.
