  We have measured temperature dependence of low-frequency Raman spectra in
CuGeO$_3$, and have observed the quasi-elastic scattering in the $(c,c)$
polarization above the spin-Peierls transition temperature. We attribute it to
the fluctuations of energy density in the spin system. The magnetic specific
heat and an inverse of the magnetic correlation length can be derived from the
quasi-elastic scattering. The inverse of the magnetic correlation length is
proportional to $(T-T_{SP})^{1/2}$ at high temperatures. We compare the
specific heat with a competing-$J$ model. This model cannot explain
quantitatively both the specific heat and the magnetic susceptibility with the
same parameters. The origin of this discrepancy is discussed.
