  It is shown that a cluster expansion technique, which is usually applied in
the high-temperature regime to calcutate virial coefficients, can be applied to
evaluate the superfluid transition temperature of the BCS-BEC crossover \`a la
Lee and Yang. The transition temperature is identified with the emergence of
the singularity in the sum of a certain infinite series of cluster functions.
In the weak-coupling limit, we reproduce the Thouless criterion and the number
equation of Nozi\`eres and Schmitt-Rink, and hence the transition temperature
of the BCS theory. In the strong-coupling limit, we reproduce the transition
temperature of Bose-Einstein condensation of non-interacting tightly bound
dimers.
