  We investigate the finite-temperature properties of attractive
three-component (colors) fermionic atoms in optical lattices using a
self-energy functional approach. As the strength of the attractive interaction
increases in the low temperature region, a second-order transition occurs from
a Fermi liquid to a color superfluid (CSF). In the strong attractive region, a
first-order transition occurs from a CSF to a trionic state. In the high
temperature region, a crossover between a Fermi liquid and a trionic state is
observed with increasing the strength of the attractive interaction. The
crossover region for fixed temperature is almost independent of filling.
