  Attractively interacting two-component mixtures of fermionic particles
confined in a one-dimensional harmonic trap are investigated. Properties of
balanced and imbalanced systems are systematically explored with the exact
diagonalization approach, focusing on the finite-temperature effects. Using
single- and two-particle density distributions, specific non-classical pairing
correlations are analyzed in terms of the noise correlations -- quantity
directly accessible in state-of-the-art experiments with ultra-cold atoms. It
is shown that along with increasing temperature, any imbalanced system hosting
Fulde-Ferrel-Larkin-Ovchinnikov pairs crossovers to a standard
Bardeen-Cooper-Schrieffer one characterized by zero net momentum of resulting
pairs. By performing calculations for systems with different imbalances, the
approximate boundary between the two phases on a phase diagram is determined.
