  Motivated by recent experiments with ultracold fermionic atoms in optical
lattices, we study finite temperature magnetic correlations, as singlet and
triplet correlations, and the double occupancy in the one-dimensional Hubbard
model. We point out that for intermediate interaction strengths the double
occupancy has an intriguing doubly non-monotonic temperature dependence due to
the competition between spin and charge modes, related to the Pomeranchuk
effect. Furthermore, we determine properties of magnetic correlations in the
temperature regimes relevant for current cold atom experiments and discuss
effects of the trap on spatially integrated observables. We estimate the
entropy and the temperature reached in the experiment by Greif et al., Science
340, 1307 (2013).
