Nonmonotonic temperature dependence of dipolar compressibility*

We calculate the compressibility of a two-dimensional gas of fermionic dipolar molecules within the Hartree-Fock approximation at finite temperature. The compressibility is nonmonotonic in the reduced temperature, $T/T_F$, exhibiting a local maximum. This effect may be detectable at currently attainable densities and temperatures, providing the possibility of direct observation of a quantum degenerate many- body effect in the ultracold polar molecule system.