We investigate the sensitivity with which the temperature and the chemical
potential characterizing quantum gases can be measured. We calculate the
corresponding quantum Fisher information matrices for both fermionic and
bosonic gases. For the latter, particular attention is devoted to the situation
close to the Bose-Einstein condensation transition, which we examine not only
for the standard scenario in three dimensions, but also for generalized
condensation in lower dimensions, where the bosons condense in a subspace of
Hilbert space instead of a unique ground state, as well as condensation at
fixed volume or fixed pressure. We show that Bose Einstein condensation can
lead to sub-shot noise sensitivity for the measurement of the chemical
potential. We also examine the influence of interactions on the sensitivity in
three different models, and show that mean-field and contact interactions
deteriorate the sensitivity but only slightly for experimentally accessible
weak interactions