  Taking into account the transverse gauge field fluctuations, which interact
with composite fermions, we examine the finite temperature compressibility of
the fermions as a function of an effective magnetic field $\Delta B = B - 2 n_e
hc/e$ ($n_e$ is the density of electrons) near the half-filled state. It is
shown that, after including the lowest order gauge field correction, the
compressibility goes as ${\partial n \over \partial \mu} \propto e^{- \Delta
\omega_c / 2 T} \left ( 1 + {A (\eta) \over \eta - 1} {(\Delta \omega_c)^{2
\over 1 + \eta} \over T} \right )$ for $T \ll \Delta \omega_c$, where $\Delta
\omega_c = {e \Delta B \over mc}$. Here we assume that the interaction between
the fermions is given by $v ({\bf q}) = V_0 / q^{2 - \eta} \ (1 \le \eta \le
2)$, where $A (\eta)$ is a $\eta$ dependent constant. This result can be
interpreted as a divergent correction to the activation energy gap and is
consistent with the divergent renormalization of the effective mass of the
composite fermions.
