  In the BCS limit density profiles for unpolarized trapped fermionic clouds of
atoms are largely featureless. Therefore, it is a delicate task to analyze them
in order to quantify their respective interaction and temperature
contributions. Temperature measurements have so far been mostly considered in
an indirect way, where one sweeps isentropically from the BCS to the BEC limit.
Instead we suggest here a direct thermometry, which relies on measuring the
column density and comparing the obtained data with a Hartree-Bogoliubov
mean-field theory combined with a local density approximation. In case of an
attractive interaction between two-components of $^{6}$Li atoms trapped in a
tri-axial harmonic confinement we show that minimizing the error within such an
experiment-theory collaboration turns out to be a reasonable criterion for
analyzing in detail measured densities and, thus, for ultimately determining
the sample temperatures. The findings are discussed in view of various possible
sources of errors.
