  The interplay of quantum statistics, interactions and temperature is studied
within the framework of the bosonic two-component theory with repulsive
delta-function interaction in one dimension. We numerically solve the
thermodynamic Bethe Ansatz and obtain the equation of state as a function of
temperature and of the interaction strength, the relative chemical potential
and either the total chemical potential or a fixed number of particles,
allowing to quantify the full crossover behaviour of the system between its
low-temperature ferromagnetic and high-temperature unpolarized regime, and from
the low coupling decoherent regime to the fermionization regime at high
interaction.
