  We investigate the time autocorrelation of the molecular magnetization $M(t)$
for three classes of magnetic molecules (antiferromagnetic rings, grids and
nanomagnets), in contact with the phonon heat bath. For all three classes, we
find that the exponential decay of the fluctuations of $M(t)$, associated with
the irreversible exchange of energy with the heat bath, is characterized by a
single characteristic time $\tau (T,B)$ for not too high temperature $T$ and
field $B$. This is reflected in a nearly single-lorentzian shape of the
spectral density of the fluctuations. We show that such fluctuations are
effectively probed by NMR, and that our theory explains the recent
phenomenological observation by Baek et al. (PRB70, 134434) that the
Larmor-frequency dependence of $1/T_1$ data in a large number of AFM rings fits
to a single-lorentzian form.
