  Motivated by the recent experiments on Bose-Einstein mixtures with tunable
interactions we study repulsive weakly interacting Bose mixtures at finite
temperature. We obtain phase diagrams using Hartree-Fock theory which are
directly applicable to experimentally trapped systems. Almost all features of
the diagrams can be characterized using simple physical insights. Our work
reveals two surprising effects which are dissimilar to a system at zero
temperature. First of all, no pure phases exist, that is, at each point in the
trap, particles of both species are always present. Second, even for very weak
interspecies repulsion when full mixing is expected, condensate particles of
both species may be present in a trap without them being mixed.
