  The zero-temperature and finite-temperature thermodynamics of two-component
Fermi gases with finite-range attractive interaction suffer from fermion sign
problem, which seems like an insurmountable problem in exact numerical
simulations. In a recent work, we find a reliable method to simulate the
thermodynamic properties of single-component Fermi gases for both
noninteracting and repulsively interacting cases based on the method of
parametrized partition function and the $\xi_E$ curve of constant energy. In
the present work, this method is generalized to two-component Fermi gases with
finite-range attractive interaction, which shows clearly that our method has
good chance to apply to various Fermi systems. From the simulated heat
capacity, we find a peak at the temperature below the Fermi temperature which
implies the pairing of fermions with different spin. At high temperature, the
simulated heat capacity approaches the classical value. The reasonable result
in this work validates the application of our method to attractive cases, which
implies a wide range of applications, from nuclear physics, BCS-BEC crossover,
superconductivity, to neutron star, etc..
