  We have measured the heat capacity of an optically-trapped,
strongly-interacting Fermi gas of atoms. A precise input of energy to the gas
is followed by single-parameter thermometry, which determines the empirical
temperature parameter $\tilde{T}$ of the gas cloud. Our measurements reveal a
clear transition in the heat capacity. The energy and the spatial profile of
the gas are computed using a theory of the crossover from Fermi to Bose
superfluids at finite temperature. The theory calibrates $\tilde{T}$, yields
excellent agreement with the data, and predicts the onset of superfluidity at
the observed transition point.
