  We present a quantitative finite temperature analysis of a recent experiment
with Bose-Fermi mixtures in optical lattices, in which the dependence of the
coherence of bosons on the inter-species interaction was analyzed. Our theory
reproduces the characteristics of this dependence and suggests that intrinsic
temperature effects play an important role in these systems. Namely, under the
assumption that the ramping up of the optical lattice is an isentropic process,
adiabatic temperature changes of the mixture occur that depend on the
interaction between bosons and fermions. Matching the entropy of two
regimes---no lattice on the one hand and deep lattices on the other---allows us
to compute the temperature in the lattice and the visibility of the
quasi-momentum distribution of the bosonic atoms, which we compare to the
experiment. We briefly comment on the remaining discrepancy between theory and
experiment, speculating that it may in part be attributed to the dependence of
the Bose-Fermi scattering length on the confinement of the atoms.

Quantum Gases;Statistical Mechanics