We study a trapped system of fermions with an attractive zero-range two-body interaction using the Shell-Model Monte Carlo method. The method provides {em ab initio} results in the low $N$ limit where mean-field theory is not applicable. The energy a
nd pairing properties are presented as functions of interaction strength, particle number, and temperature. In the interesting region where typical matrix elements of the two-body interaction are comparable to the level spacing of the trap we find large odd-even effects and signatures of shell structure. As a function of temperature, we observe the disappearance of these effects as in a phase transition.
