  We consider a realistic bosonic N-particle model with unitary interactions
relevant for Efimov physics. Using quantum Monte Carlo methods, we find that
the critical temperature for Bose-Einstein condensation is decreased with
respect to the ideal Bose gas. We also determine the full momentum distribution
of the gas, including its universal asymptotic behavior, and compare this
crucial observable to recent experimental data. Similar to the experiments with
different atomic species, differentiated solely by a three-body length scale,
our model only depends on a single parameter. We establish a weak influence of
this parameter on physical observables. In current experiments, the
thermodynamic instability of our model from the atomic gas towards an Efimov
liquid could be masked by the dynamical instability due to three-body losses.
