  We simulate the dilute attractive Fermi-Hubbard model in the unitarity regime
using a diagrammatic determinant Monte Carlo algorithm with worm-type updates.
We obtain the dependence of the critical temperature on the filling factor
$\nu$ and, by extrapolating to $\nu \to 0$, determine the universal critical
temperature of the continuum unitary Fermi gas in units of Fermi energy:
$T_c/\epsilon_F=0.152(7)$. We also determine the thermodynamic functions and
show how the Monte Carlo results can be used for accurate thermometry of a
trapped unitary gas.
