  We investigate strong-coupling corrections to the specific heat $C_V$ in the
normal state of an ultracold Fermi gas in the BCS-BEC crossover region. A
recent experiment on a $^6$Li unitary Fermi gas [M. J. H. Ku, {\it et. al.},
Science {\bf 335}, 563 (2012)] shows that $C_V$ is remarkably amplified near
the superfluid phase transition temperature $T_{\rm c}$, being similar to the
well-known $\lambda$-structure observed in liquid $^4$He. Including pairing
fluctuations within the framework of the strong-coupling theory developed by
Nozi\`eres and Schmitt-Rink, we show that strong pairing fluctuations are
sufficient to explain the anomalous behavior of $C_V$ observed in a $^6$Li
unitary Fermi gas near $T_{\rm c}$. We also show that there is no contribution
from {\it stable} preformed Cooper pairs to $C_V$ at the unitarity. This
indicates that the origin of the observed anomaly is fundamentally different
from the case of liquid $^{4}$He, where {\it stable} $^4$He Bose atoms induce
the $\lambda$-structure in $C_V$ near the superfluid instability. Instead, the
origin is the suppression of the entropy $S$, near $T_{\rm c}$, due to the
increase of {\it metastable} preformed Cooper pairs. Our results indicate that
the specific heat is a useful quantity to study the effects of pairing
fluctuations on the thermodynamic properties of an ultracold Fermi gas in the
BCS-BEC crossover region.
