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) 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. [Phys. Rev. B 70, 134434 (2004)] that the Larmor-frequency dependence of 1/T(1) data in a large number of AFM rings fits to a single-Lorentzian form.