  The strongly-correlated regime of the BCS-BEC crossover can be realized by
diluting a system of two-component fermions with a short-range attractive
interaction. We investigate this system via a novel continuous-space-time
diagrammatic determinant Monte Carlo method and determine the universal curve
$T_c/\epsilon_F$ for the transition temperature between the normal and the
superfluid states as a function of the scattering length with the maximum on
the BEC side. At unitarity, we confirm that $T_c/\epsilon_F = 0.152(7)$.
