  The momentum distribution function for the two-component 1D gases of bosons
and fermions is studied in the limit of strong interatomic repulsion. A
pronounced reconstruction of the distribution is found at a temperature much
smaller than the Fermi temperature. This new temperature scale, which equals
the Fermi temperature divided by the dimensionless coupling strength, is a
feature of the two-component model and does not exist in the one-component
case. We estimate the parameters relevant for the experimental observation of
the crossover effect.
