  We compute the fraction of closed-channel molecules in trapped atomic Fermi
gases, over the entire range of accessible fields and temperatures. We use a
two-channel model of BCS--Bose-Einstein condensation (BEC) crossover theory at
general temperature $T$, and show that this fraction provides a measure of the
$T$ dependent pairing gap. Our calculations, containing no free parameters, are
in good quantitative agreement with recent low $T$ measurements in $^6$Li. We
present readily testable predictions for the dependencies of the closed-channel
fraction on temperature and Fermi momentum.

Superconductivity;Quantum Gases;Strongly Correlated Electrons