By using new and previous measurements of the $ab$-plane conductivity $sigma_1^{ab} (omega,T)$ of La$_{2-x}$Sr$_x$CuO$_{4}$ (LSCO) it is shown that the spectral weight $W = int_0^Omega {sigma_1^{ab} (omega,T) domega}$ obeys the same law $W = W_0 - B(Omega) T^2$ which holds for a conventional metal like gold, for $Omega$s below the plasma frequency. However $B(Omega)$, which measures the thermal response of the charge system, in LSCO exhibits a peculiar behavior which points towards correlation effects. In terms of hopping models, $B(Omega)$ is directly related to an energy scale $t_T$, smaller by one order of magnitude than the full bandwidth $t_0 sim W_0$.
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