  We calculate the rate of heating through phonon excitation implied by the
noise postulated in mass-proportional-coupled collapse models, for a general
noise power spectrum. For white noise with reduction rate $\lambda$, the phonon
heating rate reduces to the standard formula, but for non-white noise with
power spectrum $\lambda(\omega)$, the rate $\lambda$ is replaced by
$\lambda_{\rm eff}=\frac{2}{3 \pi^{3/2}} \int d^3w e^{-\vec w^2} \vec w^2
\lambda(\omega_L(\vec w/r_c))$, with $\omega_L(\vec q)$ the longitudinal
acoustic phonon frequency as a function of wave number $\vec q$, and with $r_C$
the noise correlation length. Hence if the noise power spectrum is cut off
below $\omega_L(|\vec q| \sim r_c^{-1})$, the heating rate is sharply reduced.
