  We study finite-temperature magnetic phases of three-component mixtures of
ultracold fermions with repulsive interactions in optical lattices with simple
cubic or square geometry by means of dynamical mean-field theory (DMFT). We
focus on the case of one particle per site (1/3 band filling) at moderate
interaction strength, where we observe a sequence of thermal phase transitions
into two- and three-sublattice ordered states by means of the unrestricted
real-space generalization of DMFT. From our quantitative analysis we conclude
that long-range ordering in three-component mixtures should be observable at
comparable temperatures as in two-component mixtures.
