Bose condensation in the weak-coupling limit (such as classicalBCS superconductors) and the strong-coupling limit (like BECs of atoms) are understood nowadays tocan be unified into a single framework by the BEC-BCS crossover. One key feature distinguishing the BCS side from BEC is that the pairing of fermions near the Fermi surface into Cooper pairs and the condensation of those Cooper pairs happenhappens simultaneously at the same temperature.
Is there a simple argument to understand why this is so?
For a usual BCS-type interaction, at what interaction strength does this break down? Is there a known expression for the difference, as a function of interaction strength, between the temperature at which pairs become bound and $T_c$ for them to condense?