  We study thermal properties of a trapped Bose-Bose mixture in a dilute regime
using quantum Monte Carlo methods. Our main aim is to investigate the
dependence of the superfluid density and the condensate fraction on
temperature, for the mixed and separated phases. To this end, we use the
diffusion Monte Carlo method, in the zero-temperature limit, and the
path-integral Monte Carlo method for finite temperatures. The results obtained
are compared with solutions of the coupled Gross-Pitaevskii equations for the
mixture at zero temperature. We notice the existence of an anisotropic
superfluid density in some phase-separated mixtures. Our results also show that
the temperature evolution of the superfluid density and condensate fraction is
slightly different, showing noteworthy situations where the superfluid fraction
is smaller than the condensate fraction.
